You and a partner are preparing to give a presentation for a class you're taking. You're discussing the topic of your presentation, and your partner mentions some information she found while researching the topic. You think she should say something about that in the presentation. You tell her:
You should definitely bring that up.
This is a way to suggest that a person do something. Although it's a very direct suggestion, it sounds polite and helpful:
You should definitely ask for a raise after all the extra time you've been putting in this year.
To "bring up" something means to be first to talk about it in a conversation. The first person to start talking about a topic is the person who "brought it up":
I brought up the topic of Jessica, but he didn't seem like he wanted to talk about it.
The phrase "bring up ___" is like many phrasal verbs. The word "up" immediately follows "bring" most of the time, like in the last example above. But when you're using short words like "it", "her", "that", "something", etc. you put those words between "bring" and "up":
I'm glad you brought it up.
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