I had never heard the term before, so, as ever when in such a strait, I turn to Fox-Davies, who has this to say:

A compartment is anything depicted below the shield as a foothold or resting-place for the supporters, or indeed for the shield itself. Sometimes it is a fixed part of the blazon and a constituent part of the heritable heraldic bearings. At other times it is a matter of mere artistic fancy, and no fixed rules exist to regulate or control nor even to check the imagination of the heraldic artist.

He goes on rather at some length. For those who are curious, see Chapter XXVI of A Complete Guide to Heraldry, A. C. Fox-Davies, 2007, Skyhorse Publishing.