ROMs don't cost any money to use, because they are pirate copies of the games and therefore technically illegal. Here's a basic rundown.
You save a system player file on your computer, as well as a file of what game you want to play. You open them and can assign controls to your keyboard and play the game as it is on the system itself. Most handheld games, classic systems like SNES and Genesis, and even some DS games are playable. I'm not 100% sure, but I've heard of some multilayer capabilities, but it still hasn't been perfected, due to the fact that it isn't exactly easy to do. You have to have internet just to access them, but after that you won't since the files to use the game are saved directly onto your computer. They're very useful for playing classic games that either aren't easy to find, aren't available on things like Wii virtual console, or expensive to obtain. You can get tons of titles for free and it's a nice thing to have.
The downsides to them are that you risk loading a virus onto your computer. As long as you're smart about which links you go to, they can be fine to use. Just make sure the places you download stuff from is reliable. We aren't allowed to give links to such sites because of this, so I cannot do anything about that.
Not everyone considers this morally correct, but if Nintendo and other companies had this big an issue about it, they would have stopped such sites years ago. If you've got no issue with it, go ahead, as long as you're aware of the risks.
All things said, ROMs can be well worth it so long as you're smart about where to download them. If you choose to download ROMs, do so at your own risk, but they're still fun to use.
Here are my thoughts on the subject. I don't think we should completely ban the use of the terms emulator or rom etc, because they are out there, there's no point pretending they aren't...But the main thing is, I would like to avoid linking out to dodgy sites just to be on the safe side, legally and to protect users from viruses and stuff.