A polymer is a substance that has long chains of a lot of the same units at the level of atoms and molecules.

Imagine that you have a string of beads, where the beads are these units. The beads can be the same or different, but the strings are just really, really, really small, so small that we can even see these "strings" under ordinary microscopes in our schools. The strings are usually long with hundreds of beads, some are very long with thousands of beads. Because the strings are so long, they can become very tangled when they come together - imagine having strings of beads in your hands and balling them up. The "tangledness" is a large part of the reason that slime is stretchy and sticky.

Another part of the reason that slime is sticky is that the polymers in slime are made from things that can stick to surfaces, like the skin on our hands or the tabletop. This is because the polymer units (beads) themselves can be attracted to surfaces.

So both the tangledness of the "strings" and how the beads interact with other things matter when it comes to the stickiness and "stretchiness" of slime.

I emailed my granddaughters to ask them why slime is stretchy and sticky. They are 9 and 12, and they have made a LOT of slime!

Polymers are long stringy molecules that are made, like beads on a string, from little molecules [beads] hooked together.

Starch in bread and pasta is a polymer of sugar molecules.

Proteins are polymers of amino acids. Our muscles are made of proteins that can fold up short and then stretch and unfold long. That makes our muscles strong and tough.

Slime can have lots of glue in it, which makes it sticky. Polymer molecules in slime would make it stretchy.

Here are recipes for making slime:
make slime

Polymers are chemicals where each molecule bonds to the next molecule, forming a long string of joined molecules.

This is important because it causes molecules that would otherwise be free-floating and behave like a liquid to instead behave like a solid. Also because chemical bonds are very strong, these long strings of molecules can survive a lot of stress pulling on them, which is why they become so stretchy.

'Slime' generally means a liquid that contains a polymer of some kind that causes it to behave like a stretchy, sticky solid.

Polymers are molecules made up of many repeated identical subunits called monomers.

Polymers might consist of only a few monomers, or of hundreds of thousands. Each mer was an individual molecule which then reacted with another mer or the growing polymer. The properties of the polymer depend, at least in part, on the shape or structure of the polymer. In turn, the shape of the polymer depends on how the mers bond to each other. If each mer bonds to exactly two other mers, then the polymer is a long chain (also called a linear polymer).

A useful analogy for linear polymers is a plate of spaghetti - they form as a collection of many polymer chains tangled around each other. Because these chains are not attached to each other, they can move past each other. This means objects made of them can be melted and reshaped if the polymer chains can be made to move, such as by heating. Because they can be reformed with heat, these types of polymers are also called thermoplasts. The number of mers in the polymer affects the properties of thermoplasts. A larger number of mers means the chains tangle around each other more and are therefore less mobile. For two polymers made of the same mers, the one with more mers will typically melt at a higher temperature because the chains cannot move as easily. If each mer bonds to three others, then a 2D network will form, and bonding by a significant fraction of the mers to more than three other mers produces a 3D network. The connections between chains in the 3D networks prevent motion of the main chains. These cannot be melted once formed, and thus are called thermosets.

The above covers only the most basic aspects of polymers; they are not as simple as long chains or sheets though. The mers may have side groups which can have various arrangements along the length of the chain (polymer tacticity), there may be only a few bonds between chains (elastomers, e.g. rubber bands), and polymers may comprise more than a single type of mer (copolymers). These sites have information on such topics, but are a bit more advanced.

Slime has those properties because that is the definition of slime; a substance without those properties is not slime.

Without knowing the chemistry of the particular slime, it is impossible to say exactly why it is stretchy or sticky. Almost certainly the slime is a polymer though, and here are some likely possibilities.

Both "stretchiness" and "stickiness" require some higher-level concepts, so many of the details will be omitted here.'

Stretching. Essentially there are some connections between the chains of the polymer slime, but not enough that the chains cannot move past one another. Thus, pulling on the slime will make the chains move, but they cannot completely separate. While the chains are usually very tangled, pulling on the slime straightens them. However, this is an unfavorable state (in physics it would be called a higher energy state than the tangled condition), and releasing the slime allows the chains to move back to their tangled configuration. This means that slime is an elastomer, like rubber bands.

ScienceLine and this site have some further discussion on this topic.

Sticking. Sticking implies that there is some kind of connection between the slime and other objects or materials. This is also referred to as adhesion. While there are many possible contributions to adhesion of the slime, chemical adhesion due to hydrogen bonding and Van der Waals forces seems most likely. Both of these are essentially attraction between slightly positive and slightly negative parts of molecules.