Use this phrase to talk about something that you need to do, but which might annoy your listener.
I'm going to have to charge you extra for that. Sorry!
A: We're going out for a bite to eat. Why don't you join us?
B: No, I'm going to have to take a rain check.
This is similar to "going to need to". "Going to have to" is friendlier-sounding, though.
There's also another way to use "going to have to", which is just to talk about things that you have to do in the future. Here's an example: