The Big Man is the chief of each of the Feegles' clans. The most famous is Rob Anybody, chieftain of the Chalk Hill Clan. He is the bravest and - possibly - the brightest (saving, of course, any Gonnagle around), and it is to him that the other Feegles look for a PLN(1) to help them overcome any enemy/obstacle. Most of his plans involve charging and fighting, which is all right by them!
There is an irony inherent in the title, being as the biggest Big Man is still only six inches high. Any human stupid enough to point this out may well find out just what it feels like to have their knees broken and a feegle standing on their chest saying "An' who's the biggest noo, ye scunner?"
(1)...er, PLAN. Jeannie can make him read and write but she can't make him read and write well.