"Open up" means basically the same thing as "open", except that it tends to be used in particular situations. I can open up a shop or store- usually at the same time every morning. I can open up to someone about my feelings - telling them how I really feel (just "open" would not be used) I can open up a box or present with wrapping. If the police were outside an apartment or house, they might say "open up in there!", meaning the people inside should open the door, and quickly.

Sometimes, open up can also be an idiom. I could say, "I wish you would open up to me." Or "I felt I couldn't open up to anybody, not even to my best friend." It means to to talk in a free and honest way.

Gosh, Pablo.....the questions people ask here really make me think about my own language. You can "open up" a business, or a nightclub, and it would be OK, but a bit "casual".....but even here, the word "up" is not necessary - you can "open" a business. In fact, most of the times English speakers say "open up" they could say "open". There are some things which you definitely do NOT "open up"....you open the door,or the window, you open your eyes, or your heart. You open a discussion..... A policeman may bang on your door and demand that you "Open up!" Or a surgeon may "open you up". You can "open up" to people, rather than be aloof or shy or dishonest. So, I think "open up" is used to denote something general rather than specific. The surgeon "opened me up", rather than the surgeon opened my abdomen, or he opened my chest, or he opened my hip joint. My advice - avoid using "open up".