"Keep in mind" means to remember. But the word "remember" can be used in a lot of different kinds of situations. "Keep in mind" is more specific. It means to remember a fact and continue to think about it while you're making decisions.
For example, if you're planning an event for a club you belong to, you can tell the people that are helping you:
Keep in mind, our budget is pretty small.
In this case, everyone knows what the budget is, but you want them to remember that when they make suggestions for the event.
You can include "that" in this phrase or leave it out in more casual speech:
Keep in mind that you'll need to submit your application no later than Monday the 31st.
Keep in mind it's due on Monday.