Your name sets you apart from others. Great honor or dishonor can be attached to a name. In some cases, it can be a clue to your character and nature. In biblical times, people tended to live out their names as self-fulfilling prophecies, making it their lifelong goals to realize what their names meant. In 2011, there are entire websites devoted to the meaning of names.
Consult books about baby names. Two resources are "The Everything Baby Names Book" by Lisa Shaw that contains over 25,000 names, and "A World of Baby Names" by Teresa Norman. Both contain names and brief descriptions of their origin and meaning.
Look up the meaning online. Insert the name in sites like Baby Names World. The site will give you the origin and meaning of the name if it's available. For example, Baby Names World did not have a meaning for the name Jayden, but did say it was a "modern creation, perhaps inspired by the nickname Jay and the name Hayden." On the other hand, it says Olivia was invented by Shakespeare for "Twelfth Night" and was meant to be a female form of Oliver. It also says it derived from olive, a symbol of peace.
Ask a family member. Some names are strictly a matter of a significant event in a family, and only some other family member could tell you why that name was chosen for you. For example, while the name Isaiah is from the bible, it's not why it was given to Isaiah Thomas, a basketball player drafted in the 2011 National Basketball Association draft. Thomas got his first name because his father, a Los Angeles Lakers fan, lost a bet with a friend over a 1989 game. The friend insisted the child be named after a star of the other team -- who happened to be named Isaiah Thomas.