Accepted Mason 

At one time when the Lodges were mostly made up of Operative Masons a man who was not an Operative Masons could be accepted into a Lodge even though he did not work in the trade.  Thus the term Accepted.

The term Accepted, when used with Freemasonry, also seems to mean Speculative.

Before men not involved with the building trade were accepted, the term 'Operative Masons' was not needed, since up to that time all members worked in the building trade.