"to cut in on" means to interrupt someone who is speaking or doing something.
Ex: Sorry to cut in on you, but there are one or two things I don’t understand.
It's also possible to use "to cut in/to butt in" with the meaning of interrupting something:
Ex: I'm sorry to cut in/butt in, but could you explain this a bit more explicitly?
Lila cut in again, answering before he could even open his mouth.
The same phrasal verb (to cut in on) can be used to describe a sudden drive in front of a moving car in a dangerous way
Ex: She cut in on a red Ford, forcing the driver to brake heavily.
I hope it'll help.