It depends on the context in which it is being used. Open up and close up are phrasal verbs with their own meaning. But sometimes we add 'up' onto the end of open or close with no significant change in meaning.
John opens the shop at 7.00 every morning.
John opens up at 7.00 every morning.
The only difference here is that we already know that we are talking about a shop, so in context it has to come at a point in the conversation where that is already the topic. (We wouldn't say John opens up the shop at 7.00)
John really opened up last night
means that John started talking about personal matters (problems, feelings etc) that he doesn't normally talk about.
You can use closed and closed up in similar ways.
I hope this helps.