"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.