Wires carry electricity.
Switches are mechanical contacts that disrupt / allow the flow of electricity.
In all cases where wires and switches are involved, the wires allow current to flow from one place to another, and switches allow that to be controlled (off / on). This is a general and fundamental idea. Check out this primer on how electricity works, it will answer pretty much all of your electricity-related questions here.
As for what the wires in your vehicle specifically connect to, for that you should consult the service manual / wiring diagrams for your specific vehicle. This information is generally available, although you may have to do some hunting for certain vehicles if you want it for free.
Different vehicles have different wiring, although there are some generally similar concepts, which you can find on Google, and some generally common high-level functionality (e.g. accessories, running, starting, etc. described in the answers to your other question).
As an example, here is the full ignition circuit wiring diagram for the "start" and "run" mode for my own vehicle (5th gen Honda Prelude):
By the way, picking nits, when people say "ignition wires" they usually mean the spark plug / ignition coil wire set. I'd just call what you are referring to the "wires connected to the ignition switch".