Answer:
Heartbreak.
Step-by-step explanation:
When someone says that you've "taken a piece of their heart with you," it means that the speaker was still emotionally connected to the person when they left them. This is more commonly felt when two people in a relationship break up. Since it's common for people in relationships to say that their partner has "stolen their heart," when that couple breaks up, one partner hasn't severed their emotional ties to their ex yet, so they could say "when you left me, you took a big piece of my heart with you."