Have you ever listened to a song and thought, meh. Or you hated it. Or maybe you just didn't even notice it at all. Well, duh- of course you have. Nobody likes EVERY song. But I'm getting somewhere, I promise.
Anyway, then you hear that song somewhere else- maybe live. Maybe you see the singer actually perform it on TV. Maybe a friend points out how much they like it so you really listen to it and find out its a great song.
For me, it's usually seeing the song in context. For example, I didn't think much of Secrets by One Republic until I saw it on The Sorcerer's Apprentice (you know when dorky but charming Jay Baruchel makes the song out of his Tesla coils). I loved it after that. I probably wouldn't have liked Jar of Hearts but seeing it danced on So You Think You Can Dance totally changed it for me. Actually there's lots of songs that once I've seen danced on that show, I fall in love with them (Your Guardian Angel, No Air, Bleeding Love). Also a lot of songs I've come to love were on The Vampire Diaries. I think it's seeing the emotions the actors are portraying while the song plays in the background.
I've recently come to love Adele's "Rolling in the Deep" after I saw it on DWTS and then on Gossip Girl. I'd heard the song on the radio before but never payed it any attention. Now I can't get enough. If you've never heard it, you can listen to it on my playlist (at right). Forgive the cheesy rhyme, but it's an awesome song and I wanted to pass it along!