Hello Chi, It means engrossed or absorbed in something, specially one's own thoughts. You could say in other words "caught up in", "lost in thoughts","taken up", "absent-minded", "abstracted" or "distracted".

少し「夢中」みたいです。 例えば、貴方は友達に話してる。でも本当は貴方は食べ物のために思っているなら、貴方はpreoccupiedです。 濃度はないです。

i'd rather use thoughtful well depends on the situation

When you've given all your attention and all your thoughts to the one problem and forgotten or even discarded all the other. ex: She is so preoccupied with her own problem that she has been incapable of working in the last week.

pre = before; the person is occupied/worried or takes care of something before it happens :D