This is going to be a short post but will probably go a long way in helping you avoid a lot of trouble.
The words in the title simply mean “to be in Japan” but you might want to refrain from using the term 在日 (zainichi) because it’s a derogatory term used to refer to Koreans (North and South) since after the 2nd World War. While the term has gradually regained amelioration, it will serve you well to avoid using it.
Near my current office building is the Korean embassy and on an almost daily basis, we hear protestors shouting through loudspeakers trying to drive out Koreans partly due to reasons you’ve probably seen on the news since years ago. And during these protests, the term 在日 can often be heard. So, the next time you want to refer to someone who’s in Japan, you may want to say it differently, like 日本在住 (nihonzaijuu) or something else.
For more information on the term, check here.