It is difficult to define 'baggage' in human feelings terms. Maybe it's not so much difficult to 'define' but difficult to narrow down.
To most, baggage is the negative feelings or vibes you carry from previous romantic relationships to your life forward or to your next relationship(s). But why is it reduced to just romantic relationships I wonder?
Why not other form of relationships too? Friends for example and what they've done (or not done), can be baggage too. Friends probably matter more than a significant other does to some people. Friends can have a more damaging and more long lasting impact that a relationship might not.
Solution? Cut them loose. Break up. It stings and it's difficult but it's got to be done when there is no solution. Not everything works out - same applies to a friendship. You can try to keep it going but at some point you just realise it's not going to work out. You're putting in more effort in keeping it going than in enjoying it. So, leave. Let it go. Move on.