Here's a very simplified explaination...
A shielded cable has a conductive "shield, that is grounded and essentially keeps outside electrical noise from getting to your amp, where it would be amplified and sound very bad. Shields are usually made of either copper that is braided around the signal carring conductor of the cable, or a foil that surrounds the conductor.
A speaker wire, does not require a shield because the signal has already been amplified by your amp (it's at a higher voltage than the signal going into your amp), so any stray noise will not be heard through your speakers. Due to the higher voltage/power coming out of your amp, speaker cables require larger gauge wire than is required at the input of your amp.
You should always use unshieled cables to connect your amp to a speakers, and connecting speakers together. You should use shielded cables for any inputs to your amp or effects, mixer, etc. For your footswitch, you can usually use either shielded or unshielded cable (doesn't carry an audible signal, so noise isn't a consideration here)
Balanced cables have a second conductor that helps cancel noise. Because of this, balanced cables will usually be a little quieter than unbalanced, and are usually used for longer cables runs. There are impedance factors involved too, but this is the basic jist of it.
If you are unsure exactly if you have a speaker cable (non-shielded) or an instrument (shielded) cable, here's a quick and easy check. Simply unscrew the cap/strain-relief of one end of the cable and inspect the connections to 1/4" plug. One wire will be soldered to the center of the jack (signal) and the other connection is the key. You will most likely see a shield or drain wire soldered to the outer connection of the plug if the cable is shielded. Also, the outer cable jacket is usually have some text stating if it is an instrument (shielded) or a speaker cable - be sure you look there first.