I just found out about it last month. I did my research and figured out what this was about. And I can't believe I didn't know!
“A beta reader (or betareader, or beta) is a person who reads a work of fiction with a critical eye, with the aim of improving grammar, spelling, characterization, and general style of a story prior to its release to the general public.” (Source: http://www.fanfiction.net/betareaders)
I just finished my very first beta read. I already sent my feedback.
I found the experience exciting, interesting and a little scary beacuse I wanted to do a good job, give a constructive opinion and I hope I didn't hurt the author's feelings =/ I wasn't harsh but having your baby criticized can't be easy.
Author just wrote back thanking for my feedback =)
Nice first experience!