Translation:I am sorry for you.
Pole is used a lot in everyday life. Mostly it is an expression of sympathy, when something bad has happened (trivial or serious). It means "I feel sorry for you", not "I am sorry for what I did". If you're excusing yourself, you would say "Samahani".
In Northern Tanzania.it is used for an even wider range of situations. Here you can even expect to hear "Pole na kazi" (I'm sorry you have to work) when someone comes to your office, or "pole" when you look slightly tired, or are carrying something heavy.
"Pole pole" is slowly. I believe they all come from the root "kupoa" to cool down. It's an imperative "cool down" but not as in settle down (nyamaza). More like "I am wishing that you will cool down/recover from this bad/hard thing." That's also why it's inappropriate to use as "I'm sorry" and why you can say "Pole na kazi" without meaning "sorry you have to work". "Pole pole," sometimes informally abbreviated "pole," is like "go cool-ly" or as an imperative the way people use "Slowly!" in English.
It does mean "Sorry you have to work." "Sorry work is so hard on you." "I feel for you (not seeing your family so much/being stressed/... etc.) due to work." It would be used in a context that the other has just stated they must go to work now or they have a lot of work to do. (possibly other situations?)
Pole does not only mean sorry. You can also use it to congratulate someone.
My understanding is that you can almost translate it to "I feel the way you feel" or "I share your emotions". Therefore it can be used as: I share your happiness or sorrow, Simply, Pole!
I have heard it used this way in Tanzania. Would be grateful I any native speaker could confirm if I'm correct.