Significance means having the quality of being "significant" — meaningful, important. It also refers to the meaning of something. A certain date might have significance because it's your birthday or the anniversary of Princess Di's wedding.
Significance starts with the word sign for a reason. An item's significance is a sign of its importance. The significance of something can be implicit or explicit — meaning it can be clear or only known with a deeper understanding of the situation. Your perfect score on the Calculus exam might have added significance for people who know that you never even opened your textbook to study.