Eobard will take Eddie's face and do the nasty in the pasty to ensure his timeline goes on, so Eddie will die but long live Eddie.

He threatened it by holding his hand up to menace Cisco, but his hand didn't vibrate like Wells' did. Presumably, he was told to threaten Cisco and given some level of a script or the like and so he knew to raise his arm like that because Harrison Wells is consistent across timelines.

I was Daewoo'd.