A density is the amount of material (its mass) in a given volume. For example, the density of pure water is 1 kg/L. That means that each liter of pure water has a mass a 1 kg. When minerals dissolve in water, they separate into ions (positively or negatively charged atoms or molecules). For example NaCl (salt) dissolves to form Na+ and Cl- ions. There can be a lot of Na+ and Cl- and other ions dissolved in saltwater and each of these ions has a greater mass than water. What that means is, if you have extra ions in water (instead of just pure water) those ions take up part of the volume of water and make it heavier. If you have a liter of pure water, it will have a mass of 1 kg. If you have a liter of salt water, you will have a lot of pure water plus some other ions that have a greater mass than water, making the whole liter of saltwater have a mass greater than 1 kg. So ions increase the density of saltwater.

When ions get dissolved in water, they float along with the water molecules, but they don't increase the volume very much. However, density is mass divided by volume, so since we've added a lot of mass (the ions) without changing the volume very much, we get water that has a higher density.

An important concept when thinking of floating is Archimedes' Principle. It states that objects more dense than water will sink, while objects less dense will float. This makes some sense - a rock would sink in water, but styrofoam wouldn't. If we were to increase the density of water (by adding ions), we could make it easier for something to float in the water.

Most ionic substances are denser than water, and as a result, they increase the density of the solution they are dissolved in. Obviously, this affects what floats and what doesn't.