Your robot needs power somehow, so you need a power system.
Batteries are the most common ways to power robots. The best choice of battery is usually LiPo. It allows for very high amp draw and lasts a long time.
Lipo batteries come with a certain number of cells, each of which is 3.7v but is usually charged to 4.2. For example a 3s (s is for cell) lipo is rated at 11.1v, but can be charged to 12.6v. Lipos can be dangerous. If they are shorted, they will blow up. Heres an article about lipos.
SLA, sealed lead acid, batteries have very high capacity, and an extremely high momentary amp draw, but a very low continuous amp draw, which is why they are used to start cars.
NiMH batteries are getting kind of out of date these days, so only use them if a competiton (*cough* Scioly *cough*) disallows both lithium and lead batteries.
Lithium Iron Phosphate, LiFePo4 batteries are pretty hipster these days, not many people have actually used them, they're just talked about a lot, so they have the potential to be pretty good.
Sometimes you need a different voltage that your battery puts out, which means you need a regulator. BEC, or battery eliminator circuit's are a good way of stepping down any voltage form 7-24 V to 5V. If you need something else, you will need a buck converter.
I do not recommend using wall power, it is dangerous, and difficult to use. If you do, use a PSU, and probably one from a reputable brand like Meanwell.
Connectors to your batteries are useful so you can easily remove them when you want, but also they don't come unplugged accidentally.
XT-60 is my reccomended battery connector for anything decently sized. JST is acceptable for smaller sizes, but XT-60 is always a good option. Actually I've started to really like phoenix connections when you're dealing with really large amperages.
-lmr