Galumphing is moving in a heavy, clumsy manner, often at (comparatively) high speed. (Galumphing is traditionally a form of running, but modern usage allows you to galumph slowly if the mood strikes you).
From Lewis Carroll's Jabberwocky, 1872. He most likely intended it to be a combination of gallop and triumphant, although I don't believe that this was ever officially confirmed by Carroll himself.
He left it dead, and with its head
He went galumphing back.
Heffalumps galumph. Woozles do not.
WordNet 1.7 defines galumph as "leap around playfully, like young primates". Don't know where they got that from -- but if you see this word in the context of primates, maybe the author is referring to playful leaping.