Like any dissolution process, dissolving sugar in Kool-Aid results in a solution, i.e. a homogeneous mixture of two or more substances. (Also note that a solution is special type of mixture, one whose constituents cannot be differentiated by sight.) The substance which makes up most of the solution (here this is the Kool-Aid) is called the solvent, and the substance(s) which dissolve are called solutes.

During dissolution, the bonds between particles of the solute are broken and the particles are distributed throughout the solvent. In the case of sugar, the solute particles are molecules, and the solvent is water (Kool-Aid is basically some stuff dissolved in a large amount of water already). The intermolecular bonds keeping the sugar molecules next to each other are overcome in favor of formation of bonds between sugar molecules and water molecules ( schematic picture ). Note that the sugar molecules remain intact; the bonds between atoms in the molecules are not broken during dissolution.

(As an aside, the "formula unit" of the solute does not necessarily stay together. In dissolving ionic compounds, the positive and negative ions are separated ( dissociation ). Consider dissolving table salt in water, an ionic compound comprising positive Na+ ions attracted to negative Cl- ions. Such a solution will contain Na+ ions bonded to water molecules and negative Cl- ions bonded to water molecules, but not the neutral (NaCl) unit.)

For more advanced students:
So far, the discussion has ignored any of the chemistry and thermodynamics behind the formation of solutions. This is an extensive topic in itself, but here is a brief overview.

To form a solution, the energy of the solution must be less than that of the separated solvent and solute. If performing this mixing without special equipment, our environmental conditions will be those of isothermal mixing and constant pressure, and the energy change (dG) given by
dG_mix = dH_mix - T*dS_mix
(T = temperature).

There are two contributions to the energy change:
(i) dH = change in enthalpy, which is energy due to bonding, and
(ii) dS = entropy, energy related to the number of arrangements of the particles.

Bonds between solvent and solute particles can be either more or less favorable (i.e. lower or higher in energy) than solvent/solvent and solute/solute bonds. If lower in energy (dH_mix < 0), then solution formation will be favored; if higher in energy (dH_mix > 0), then formation of a solution will be disfavored and the second component, from entropy, will need to be larger to form a solution.

Entropy is a tricky concept, but here it can be considered to be related to the number of arrangements of particles. When the solvent and solute are on their own, separated and pure, each has only one configuration (think, each particle of solvent or solute can only be surrounded by other particles of solvent or solute). After combining them, there are many other configurations (in very simplified example, say 1 solvent molecule next to 5 solvent molecules and 1 solute, or next to 3 solvents and 3 solutes, etc.). Thus, the entropy of the system increases by mixing and (because of the negative sign in the dG equation) system energy decreases.

There is far more to be said, but this answer can't include a full thermodynamics course. For more information, see this video series .

Let’s assume that there is a lot more Kool-Aid than sugar in a glass. Kool-Aid itself is actually a mixture of sugar, water, dye, and flavoring. So when we add our sugar crystals, the water molecules and sugar molecules in the Kool-Aid will come in contact with the surface of our pure sugar crystals. Since sugar molecules and water molecules are attracted to each other, the water molecules will slowly begin to pull away sugar molecules at the surface of the sugar crystals. Molecules of sugar that are carried away will bounce around with the water molecules and already-dissolved sugar molecules in our container. Eventually, the water and sugar molecules will completely mix into what is called a homogeneous solution - a solution which has a constant concentration of sugar and water at every point in the solution. It is at this point that you will no longer be able to see individual crystals of sugar in the glass.

I said earlier that we assumed there was more Kool-aid than sugar. This is because the sugar can only dissolve in water if there are enough water molecules to surround the sugar molecules. Once there are too many sugar molecules and not enough water molecules, sugar stops dissolving. This is called the limit of solubility.

A sugar molecule consists of a line or ring of carbon atoms connected to alcohol (oxygen-hydrogen) groups with one alcohol group on each carbon. Oxygen exerts more of a pull on the electrons in a water molecule than hydrogen does, which causes the oxygen to accumulate negative electric charge while the hydrogens accumulate positive charge, creating an electrically-aligned molecule called a dipole. Alcohol groups in sugars behave the same way, because they are made of the same two elements as water. When a crystal of sugar is placed into water (Kool-Aid is mostly water), the oxygens in the water begin interacting with the hydrogens in the sugar, and the hydrogens in the water interact with the oxygens in the sugar. This weakens and removes the interactions between the sugar molecules with the other sugar molecules in the sugar crystal. As the sugar molecules are pulled away from the crystal, the crystal dissolves, leaving the sugar in solution instead of in its solid, crystalline, state.

Since Kool-Aid is mostly water, the sugar would most likely dissolve without changing the Kool-Aid much, except for making it sweeter. However, continuing to add sugar into the Kool-Aid would eventually result in what we call "saturation", where no more sugar will dissolve in the solution. At this point, any more sugar that is added will simply sit at the bottom of the liquid if no stirring is happening.

Fascinating question! Before I answer, I want to briefly touch on how Kool-Aid mix works.

Kool-Aid is a flavored drink mix powder that is added to water to make a liquid concentrate. Its main ingredient are sugar and fructose, another type of sugar found in fruits and vegetables. Next is citric acid, a sour flavoring agent from citrus, followed by ascorbic acid, another name for vitamin C. There is also calcium phosphate, like a calcium supplement, that acts as a preservative. After those, the rest of the ingredients are mainly artificial flavors and artificial colors. Overall, this is a simple ingredient list.

The fascinating part of Kool-Aid to me is that despite sugar products making up the first two main ingredients, Kool-Aid typically is "unsweetened." This means that despite sugar in the ingredients, the container still asks for more sugar to be added. Which leads to your question about what happens when that sugar dissolves in the Kool-Aid and water mix. The Kool-Aid mix and sugar added to water creates a solution, or a mixtures where two or more substances are well mixed or homogeneous. In this case, the Kool-Aid and sugar are the solutes dissolved in the liquid water, the solvent. But you should know that liquids can also be dissolved in other liquids, solids can be dissolved in solids, and gases can be dissolved in liquids.

Sugar is a polar molecule, meaning there are places on its molecule structure where it is slightly more positive and places where it is slightly more negative. These two areas attract one another, and because there are many of these areas and the molecule is somewhat large, the sugar is a solid. Water is also a polar molecule. In water, the positive and negative areas have a stronger attraction than the attraction of the sugar molecules, causing the sugar to dissolve. Energy is also required to help break the bonds that keep sugar solid. I will not go into details except to say that some of that energy comes from the attraction of the water molecules to the sugar molecules. You can think of this as being similar to how you can cross the monkey bars by holding tightly to the bars, but Earth's gravity will always pull you down to Earth's surface the moment your grip weakens. This is why things like sugar and salt will dissolve in water but sand will not dissolve, because the molecules in sand are more tightly bonded than the strength of the attraction of water.

So as you add sugar to your Kool-Aid and water mix, the sugar and Kool-Aid mix both dissolve into the water.

I will close with saying that there is a limit to how much sugar can dissolve in water. Higher temperature water usually increases the amount of sugar that can dissolve, while cooler temperature water usually decreases the amount of sugar that can dissolve. So you can actually reverse the process of dissolving sugar. If you dissolved sugar in hot water until no more sugar was dissolving, then carefully cooled the water without stirring it, the sugar will remain dissolved in the water. However, if you had dropped a few grains of solid sugar crystals into the water solution at that moment, those sugar crystals would have started to grow into larger crystals, thus turning the dissolved sugar back into a solid form. This process as how rock candy is made. The dissolved solution can also be turned back into solid sugar if the water is evaporated. The water will be removed into the air, and the remnants in the glass will be sugar. This process is called a physical change. The physical form of the sugar is changed, but its chemical composition is not changed.