When you don't like/hate your significant other and want to break their heart cause you don't want to be with them anymore. This could also be interpreted as ending your relationship with someone. Most relationships end because your significant other is either:
-Bad in bed
-Not a good boyfriend/girlfriend
Gabriel (The boyfriend) : Hey Kelly, you're the best girfriend in the world and I love you forever :*.
Kelly (The girlfriend) : Fuck you Gabriel, I wanna party and have sex with 20 different guys all at once. I'm dumping you!
This is a perfect example of "Dumping someone"
In this example, Gabriel got dumped but his now ex-girlfriend Kelly.