Definition from Wiktionary, the free dictionary
Probably connected with pumba (“lump; clod of earth”), following a sense of “be lumpish, heavy”
- To be foolish, silly, weak-minded, careless, negligent.
- pumbaa kazi — take no pains about a job, do it carelessly, be idle
Related terms 
- pumbaza (“befool, make a fool of, treat as a fool, deceive, play jokes upon”)
- jipumbaza (“be stupid on purpose, pretend to be a fool”)
- pumbazwa, pumbazika (“be made a fool of, be duped”)