Alpha carbon

Carbon can be found in the Alpha or Beta form.

An alpha (α) carbon is the first carbon to which a functional group (i.e. Alcohol, Aldehyde, Ketones and carboxylic acids) is attached.

We can have more than 1 carbon in a structure which has a functional group attached to it and therefore we call the second carbon with a functional group, a Beta Carbon. 

Refrences 

Stryer et al p. 337