A Maxicon is an elementary semantical unit, in which a linguistic phrase conveys both an explicit meaning, and a second implicit sense, which contradicts the explicit content.
An excellent example can be found in the recent Max Mosley interview, conducted by Maurice Hamilton for the August edition of F1 Racing. Discussing FIA President Jean Todt's handling of the Bahrain Grand Prix fiasco, Max comments:
"I don't want to criticise poor Jean."
The explicit meaning expresses a disinclination towards censure, whereas the implicit content is:
"Poor Jean really isn't up to the job."