Throughout the life of the series, the Doctor has had a companion (usually a young woman) travelling with him, but his relationship with each companion ends badly--they're lost in some way that he can't rescue them. When the Doctor Who series was brought back in 2005, Rose (the blonde girl in the meme) was his new companion. They had a relationship bordering on romantic (they were in love but kept it platonic) and the relationship ended when Rose was trapped in another dimension (the wall in the meme is the dividing line). He had no way to rescue her without destroying the universe, so he had to leave her there. The Doctor Who character is resigned to fate whenever he loses a companion, so the meme is saying he's going move on because Rose was a little clingy (which she was).
I hope that helps :)
Caption this Meme
