To accumulate means to gather, usually in large quantities. Let's hope your boyfriend is not the type to accumulate girlfriends.
The root of accumulate is cumulus which means "mound" or "heap." You might have heard of cumulus clouds, those big fluffy clouds that look like giant piles of whipped cream. Think of these heaping helpings of clouds when you think of accumulate. The money in your savings account accumulates interest, though these days you won't accumulate much wealth that way! Police accumulate evidence until they have enough to charge someone with a crime.