So in Season 1 Episode 11, after Elena crashes her car, Damon takes her to Atlanta to visit a bar run by the witch Bree. Bree pretends to be friendly to the pair, but secretly calls Lee, Lexi's boyfriend, who wanted revenge on Damon for killing Lexi. Elena gets Lee to change his mind, and Damon goes to confront Bree, who says that Lexi was her friend.
Ok, Bree says, as a sort of defensive measure, that she is 'full of vervain', because she puts it in all her food/drink. So her blood is off-limits to Damon, as a vampire. So if Damon drinks her blood, he'd be burned/incapacitated by the vervain.
Just like in Episode 20, where Giuseppe (the Salvatore brothers' dad) spiked Stefan's drink with vervain to trap Katherine. When she drank Stefan's blood, she was incapacitated by the vervain.
But when Damon killed Bree, he grabbed her heart and ripped it out of her body. So his hand came into contact with her blood which was 'full of vervain'. So why didn't his hand burn? He should have been hurt by the vervain.