Keep up is a phrasal verb.
Keep up means
- to move or progress at the same rate as someone or something else.
 - to continue the course of action.
 - to maintain a relationship with someone.
 
Keep up in the context of moving or progress at the same rate as someone or something else.
- He needs to run faster, so he can keep up with the group.
 - Tim needs to sell more cars this month to keep up with Maxine’s sales.
 
Keep up in the context of continuing the course of action.
- Keep up the good work.
 - If you keep up the good work, they will promote you.
 
Keep up in the context of maintaining a relationship with someone.
- It is important to keep up a friendship, you can do this by calling or texting your friends to check on them.
 - We meet once a month for dinner to keep up our friendship.