In organic chemistry, alpha, beta, gamma, etc. are usually used to refer to the position of functional groups relative to other functional groups. Groups which are adjacent to other functional groups are called alpha. Groups attached to the next carbon over (2 carbons away from the functional group) are called beta, etc. For example:
In alpha amino acids like glycine (H2N-CH2-COOH), the amino group is on the alpha carbon, the carbon directly adjacent to the carboxylic acid).
In beta-mercaptoethanol (a.k.a. 2-mercaptoethanol, HS-CH2-CH2-OH), the thiol is in the beta position relative to the OH (i.e. there are two carbons between the thiol and the alcohol).
So, given these definitions of alpha and beta, what is special about the alpha hydrogens of a ketone?