The conductors inside the cable come in a variety of sizes. The purpose of this is due to the amount of current which has to travel through the conductor in order to operate the load. For example, a circuit operating a single light bulb will only carry a small amount of current because the light bulb only draws 1/2 an amp. But if that same circuit were to operate 100 light bulbs, now that circuit needs to carry 50 amps current. This would require a larger conductor size to handle the heat that is created. Therefore proper wire sizing is critical.
Most 120Vac household circuits are fine using a 12 or 14 gauge wire. The smaller the gauge Number the larger the conductor size.
So when your needing a three conductor cable to wire up a basic 2-way switch, you will need a 14/2 w/ground cable. What that number means is 14 gauge (wire size), 2 conductor which also includes a bare ground wire. The 2 conductor only refers to the insulated wires and not the ground.
So 14/3 w/ground represents 14 gauge wire, 3 insulated conductors and 1 bare copper ground wire.
Now some wire manufacturer's will put a green insulation on their ground wires but then it will typically count as a conductor. Kinda confusing isn't it. But try not to put too much thought into it. Most common house circuits are very basic and thats all we really care about for now.