The addition of 'up' can sometimes make the action more complete. It changes a simple verb into a complete action, so that you don't need another noun to be the object of the verb.
For example, a mother would say to her children. 'Come on, eat up!' This means 'eat everything that is on your plate'.
Or after a party, you would say that you need to 'clear up'. That single phrase encapsulates the whole idea of clear all the glasses off the tables, clear all the rubbish off the floor, clear all the plates off the kitchen worktop etc etc. Simply 'clear up'. Neat, isn't it?