meaning - Phrase Question "Be preoccupied with"

One question on meaning of the phrase "be preoccupied with", I am not a native speaker and tried to find out the accurate meaning and nuance on the web search, but could not.
I have seen that a native speaker use this phrase when he excused for a delayed response to a client as in "Sorry for my late feedback, we are preoccupied with many things in the past few weeks". I understand that this means "I have been busy for many things to do". But there is no any results relating to what I expected. Would my understanding on the meaning be correct?