All companies formed in the past 150 years, under the various Companies Acts (Companies Act 2006 being the most recent) must have articles of association.
The company articles of association are the internal policies, rules and procedures that the directors and shareholders must adhere to. Shareholders delegate all powers to the directors who in turn make decisions at board meetings. Shareholders will require assurance that any decision making by the directors follows a written procedure. The articles duly provide a detailed decision making and voting procedure together with rules on appointing directors, the distribution of profits and general administration.
A more simplistic explanation is they provide an aide-memoire for the directors of the main statutory regulations imposed by the immense Companies Act 2006 legislation. The articles are in reality a summary of the main points of the Companies Act 2006 that a small limited company should be focused on.