All companies start out as private enterprises. That means there are only a handful of shareholders in the firm, and sometimes just one. But at some point, the company's owners might decide to 'go public', and put their shares up for sale on a public exchange for anyone to buy.
There are all sorts of reasons for going public. One of the biggest is to raise capital for the firm. But sometimes publicly-traded companies decide that they don't like the limelight after all, and they decide to take their company private once more. Again, there are all sorts of reasons for making a move like this. One of the biggest reason is ... control.