Look up means to search for something online or in a dictionary, textbook etc.
Usually you look up something that you don't know. 

For example, you can say "I am going to look up this word" and that means you are going to find its meaning. If you say "I am going to look for this word" that means you have a text and you want to find the word in the text. 

Look up words in dictionary, newspaper or book 

Look for your friend in a party or somewhere