Hey cjacek, those are crimped spade connectors or terminals, pretty common in consumer electronics, automotive and industrial applications.
As miroslav said, it can be a bugger to remove by uncrimping the metal sleeve that goes around the wire beneath the plastic, but it's usually doable with some finesse. Easier to cut the wire, strip it back and attach a new connector, you can use pliers or some improvised tool to recrimp, but a crimping tool is probably preferable, they are dirt cheap especially those combi crimper/wire stripper tools that most places that sell the connectors should have too.
Without stating the obvious, if you do cut the wire, make sure you have enough slack that the connector will still reach the terminal, or you'll need to extend the wire somehow, but that's probably an easier job than trying to uncrimp the old one. Hope that helps too.