To look up a word or a fact is to search for it in a book or online. You do not know it, so you go and find it.
It splits round an object, so you look it up. Before search engines this meant a dictionary or a directory, and the phrase has survived the change of technology completely. There is a second sense meaning to visit somebody you have not seen for a while, as in look me up when you are next in town. And things looking up means the situation is improving, which is one of the warmest phrases in English.