1. to unwrap something; to open something.
> Yes, I want to open my presents up.
> I can't wait to open up my presents.

2. to begin examining or discussing something.
> Do you really want to open it up now?
> Now is the time to open up the question of taxes.

3. to reveal the possibilities of something; to reveal an opportunity.
> Your letter opened new possibilities up.

4. to start the use of something, such as land, a building, a business, etc.
> They opened the coastal lands up to resort development.
> We opened up a new store last March.

5. to make a vehicle go as fast as possible. (As in opening up the throttle.)
> We took the new car out on the highway and opened it up.

6. to make something less congested.
> They opened the yard up by cutting out a lot of old shrubbery.