A PCB is the part of an arcade game that actually has the game on it. The term properly means "printed circuit board", but it is one of those terms that is almost always used in the short form. I have yet to ever see anybody use the full form in a conversation. The terms boardset, CPU, and MPU are also used interchangeably with PCB.
A game PCB will generally have several processors on it, with Z80s and 6809s being common on older games, and 68000s being used on the majority of newer titles. Some games don't have a processor at all, and are done entirely with logic gates and analog circuits, games like Pong, Computer Space, and Shark JAWS fall under that category. The game's code is usually stored on a bank of EPROMs, or a hard drive in the case of some newer titles. The board is usually rounded out by several banks of RAM chips. Most older games have their RAM soldered right onto the board, but I have seen a few newer titles that actually use standard PC RAM.
The PCB usually interfaces with the rest of the game via an edge connector. If you don't know what an edge connector looks like, then take a look at an old Nintendo or Atari cartridge, they have edge connectors as well. Almost all games made after 1986 have an edge connector that is compliant with the JAMMA standard. That means they can easily be changed back and forth between machines with no rewiring. Older titles often had unique edge connectors, or at best were compatible with other games from the same manufacturer. Some games don't use an edge connector, and instead they use tons of little "feature connectors" that each have a few wires on them. Titles like this are an absolute nightmare to rewire from scratch, and you might want to avoid them, (Xybots, Gauntlet, and all Century Video System games are like that).
A lot of people collect these PCBs, as they essentially contain the game, and they take up a lot less space than an entire dedicated cabinet. I have about 50 of them myself. As long as you have a working PCB, then you can usually build yourself a game with off the shelf parts. The only real exception to that is laser disc games, and games that use an X-Y monitor, because they also require uncommon parts that are long out of production.
When purchasing a game PCB you should be aware of a few things. The first one is that "untested" usually means broken. Broken PCBs can sometimes be repaired, but it isn't always easy. Older PCBs are much easier to repair than newer ones are. I have seen a repaired Centipede PCB that was shot with a gun five times. But on the flip side of the coin, most shops won't even accept anything for repair newer than about 1985.
You should also check to make sure that you are getting the entire PCB assembly. Some games used multiple PCBs (Gorf had 5 of them), and others had a separate sound card. Missing parts like that are going to be hard to find unless you have a really common game (like Defender or Ms. Pac-Man).