Baggage is when there is something from your past that is blocking your present and your future.
Baggage is when you replay a remark or conversation over and over in your head, imagining all the other ways you could have handled it... and all you focus on is that past moment instead of focusing on what is going on NOW and what you want to do about it.
Baggage is when you judge a person based on how he used to be, instead of seeing that person for who he is today. This can work for or against you depending on the situation: if the other person used to be horrible, but he's changed, then you're judging him based on your negative memories of him. And it works in the opposite way, too: if a friend treated you well in the past, but now she treats you like garbage, you might put up with the bad treatment because you keep hoping she'll be the way she used to be. Either way, you're not seeing the person accurately for who they are now.
Even good past moments can become useless baggage. Like playing the "remember when" game with yourself and comparing your present reality to something in the past, and where you feel happier remembering the past then you do living your present life. So instead of working on making today more satisfying, you wallow in how great yesterday used to be.
Sometimes we carry around other people's baggage. This happens when we allow other people to project their opinions, beliefs, and needs onto us, and we absorb their baggage and accept it as gospel without question. If we aren't self-aware enough to realize that we are taking on someone else's "stuff" instead of thinking for ourselves, we run the risk of living someone else's life instead of our own.
We dress up our "baggage" and try to make it prettier when most of the time, it's pretty ugly. In other words, we often make excuses about our baggage, whether to others or even to ourselves. We even deny that we HAVE any baggage. Read the average personal's ad -- everyone claims to be baggage-free and they certainly don't want to meet anyone with any baggage. But that's unrealistic, because we all have some of it... the question is, how much do we have and what are we doing to lighten the load a bit? You can't fix something by ignoring it and hoping it will go away on its own, so the only way out of "baggage claim" is to pick up your baggage and deal with it.
Our baggage is like a weight we carry, like a millstone around our own necks. When you are carrying around that baggage, instead of releasing it and moving on from those past moments, you are cluttering up your mind and heart and soul and making it difficult to move on with your life... who could move forward with that much extra weight?
The only baggage we should be carrying is a suitcase full of clothes on our next vacation. All the other baggage is a complete waste of energy. I'd rather try to "travel light".