A predecessor is something that came before the current version. The person you replaced at work is your predecessor, just like Pac Man is the predecessor of modern video games.
If you break the word predecessor down to its Latin roots, you get pre, meaning "beforehand," and decessor, which means "retiring officer." So that's how we get to our definition of "someone who has held an office or position before the present holder." But predecessors aren't just found in the business world: these days predecessors include our ancestors, earlier car models, and all kinds of other forerunners.