question on size of object

While reading the peterson field guide to the stars and planets, it gives
the diameter of M31 as 2 degrees and 40 arc minutes. It further states the
diameters are a guide to the size of the object when seen through a 6-8 in
reflector.
What is the normal diameter when looking through the eyepiece? Can someone
explain to me what degrees and arc minutes are?
thanks