Simply put, most cheat tools allow you to easily replace certain values in the program with a different value while it's running (such as 50 gold with 1000000 gold). This often requires some trial-and-error as well as general computing knowledge on the part of the hacker. For more on hex editing, please read this Wikipedia article.
Another type of "cheat tool" is using a hacked version of the game, where someone modified the game in a way that permanently changes a value for anyone using that game version.