"Modules" are self-contained bits of code. Each module (generally) performs a specific task. In essence, "modules" are Node's version of "libraries". They're pretty much the cornerstone of Node so yes, they're rather important.
You can't make a bot without using at least the built-in modules (like net which provides network communication). You could definitely make a bot using only the built in modules, but only if you're insane. You'd have a lot of work ahead of you if you decided to make a bot without using any third-party modules.
For example, the steam-user module exposes an interface with which you can log into and interact with Steam. You could do that yourself, but then you'd need to implement the crypto, protobuf, protocol, and more yourself. Not a small task by any measure.
