Translation:To ask for
In Tanzania, it is very normal to ask for something with 'ninaomba', e.g. at the market. In Kenya, if you say 'ninaomba ndizi' you are understood as begging for bananas. In Kenya one would use 'nipe ndizi' (give me bananas), but this sounds a little bit rude in Tanzania.
"To ask" and "to ask for" are different verbs, even in English. You can ask a question, but if you ask a glass of water people will look at you funny. Likewise if you ask for a question it means something different.
In Sawhili, kuomba is ask as in "to request" or "to beg". A quick search suggests kuuliza is "to ask (a question)".
Just to add on to what juryrigging has said, "kuomba" is one of those words which are not easy to translate. Though we can think of the word to mean "to beg", my understanding is that "to beg" would be too strong and simply "to ask" is too weak. We need something in between. The main point to get from this is that "kuomba" is used to mean "to ask for (sth)" in a polite/kind way. So, it can be thought of in English as adding a "please" to your asking.
There is however one example in English which seems to match closely to the meaning of "kuomba" but bear in mind that this is old usage. The word is "pray" as in ,
"I pray thee, do tell." to convey that you are kindly asking the person to tell you whatever it is that was in context.
I hope that helps.
Maybe the best contemporary English equivalent would be "to request"? Good explantation btw.
to plead (another option of theirs, which I like a little more as it could be from any social class; while beg has a strong connotation in English)