"Going into" a topic means to speak about it.
You can use this phrasal verb to talk about what someone said:
Did she go into any details about our new health benefits?
You can use this phrase to talk about what you're saying as it's happening:
Do you want me to go into a few more details?
There's another phrase which is similar:
I don't want to get into it.
"Getting into" a topic means talking about something that's complicated or annoying to explain.