Looking at swag from a distance, it can be seen simply as confidence, but upon closer inspection, it is slightly more intricate. For me, it is going into a meeting, knowing that you will provide valuable input. It is understanding that if I am in a pickup basketball game, my team will always be competitive, and won't get blown out. It's going into an interview unsure what questions might be asked, but confident that I have the experience to provide a good answer.
Swag is knowing what your strengths are, understanding how to use them, and executing in appropriate situations with the goal of performing at a high level. It is the elimination of self doubt, and the ability to handle any obstacle thrown your way. It shouldn't be confused with cockiness; being respectful of the abilities of others, as well as being open minded and willing to learn are necessary. Swag involves taking everything learned into effect and using it to do your best.
Bring that swag on the daily. It'll do you good.