A majority shareholder (or group of shareholders) can cast the majority of votes at a general meeting of a company, and therefore controls all important aspects of running the company such as the appointment of directors.
This affects the rights of minority shareholders who are effectively deprived of their say in the running of the company. If a majority exists, then this can reduce the value of ordinary shares held by other shareholders, as the rights attached to these are less effective — in extreme cases they may as well be non-voting shares.
The majority may be an individual, a company or a group of connected entities (e.g. companies in the same group, or members of a family): any group that can reliably cooperate.