English has numerous phrasal verbs, or verbs that appear with a preposition, and usually also have a different meaning than the verb without the preposition.
However, sometimes there is no big change in meaning.
In these cases, up a lot of times means "completely" or "thoroughly":
Clean this mess up = Clean the mess completely.
Read up on your history, you don't know what you are talking about = Read thoroughly on your history (implication: you need to be educated)
Up, while it typically means "above", can also mean "toward with the intent of ending the motion near X" with verbs of motion.
Pull up a chair = Pull a chair toward me.
The cat snuck up on the mouse = The cat snuck toward the mouse.
Walk up to the counter = Walk toward the counter.
And of course there's verbs where up changes the meaning into something related, but different.
I added another task to my list. (My task list gained a task.)
The numbers don't add up. (The numbers don't total what I expect.)
I dug a hole for the firepit. (There's a spot somewhere missing some dirt.)
I dug up information on the suspect. (I went through a lot of information to find things I wanted.)