Often you're exposed to music because a friend, family member, or significant other plays it around you. For example, an ex of mine was really into Jethro Tull. Not exactly my cup of tea, but just because I didn't like it didn't mean he stopped playing it around me. Consequently, I know a lot of their stuff even though I'm not a fan.
Sometimes you hear a few songs by a band and aren't that impressed, but listen to more because it's highly recommended by someone whose opinion you value or the band itself has a good reputation.
Other times you may return to something you intially didn't like, to give it a second chance. I think that's cool. You may end up appreciating something that you just weren't into before for whatever reason.