A listed company is said to have been taken private when it is bought by someone other than another listed company, and its listing is cancelled.
Companies are most often taken private by directors, founders and private equity companies.
The rationale for taking a company private is that the buyer feels that they can run the company better without the need to justify their decisions to other shareholders. In the case of founders, one often also suspects a sentimental attachment to the business they created.
There are a number of reasons why someone might feel that they can run a company better as a private company. They may find it difficult to convince other shareholders of the benefits of the strategy they want to follow. They may also simply feel that the costs of a listing and the management time it takes are simply not worth it.