The symbol of the Laurel wreath was traditionally given to scholars, artists, athletes and soldiers in Ancient Greece as symbols of excellence. In the SCA, the Laurel is awarded to those who excel in a particular area of arts and sciences, and it's in the job description for them to pass on knowlege to others. These people also judge A&S competitions, pass on recommendations to the Crown as to who future laurels should be, and are examples of courtesy and chivalric conduct. A Laurel may take on an apprentice to train up to 'laurelhood', often in a particular field similar to their own.
Becoming a Laurel (or any type of peer) takes about 10 years of dedicated work, on average.