An advantage is like a head start in a race; it's that thing that gives you a better chance.
The noun advantage also refers to a reward or benefit of some action or event. Being sick with the flu had the advantage of kick-starting your diet because you didn't feel like eating much. If you leverage the benefits, you are taking advantage of the situation. If you go on a business trip to Hawaii, you could take advantage of the opportunity and spend an extra day or two on vacation.