Bookkeeping is keeping track of a business's financial transactions. Most bookkeeping these days happens on computers rather than in actual books.
The activity of keeping your own financial records and the job of doing the same thing for a company are both considered bookkeeping. Some people teach themselves basic bookkeeping and others hire experts to do it for them. The word bookkeeping comes from the sense of book that means "record" or "written document," and it has the distinction of being one of very few words in English with three consecutive double letters.