A good trencher-man. A good eater. The trencher is the platter on which food is cut (French, trancher, to cut), by a figure of speech applied to food itself.
Oh, how wretched Is that poor man that hangs on princes favours! There is, betwixt that smile he would aspire to, That sweet aspect of princes, and their ruin, More pangs and fears than wars or women have.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Trencher from Infoplease: