“Pack up” is almost the same as “pack”: to put your clothes and other things into boxes or a suitcase, for the purpose of moving or travel. We sometimes add “up” for emphasis, or to show completeness. Even though it doesn’t change the meaning much, English speakers add “up” to their verbs quite often.

Let’s pack up early so we can just relax after. 

Some other phrasal verbs with 'up' include:

• finish up
• clean up
• hurry up
• listen up to (something)
• write up  (something)
• read up on (something)
• drink up
• eat up
• draw up (something)
• think up (something).