Shareholders are the owners of a limited company. A share is a recognised ownership currency and it is used to represent a stake in a particular company.
The vast majority of UK limited companies have a share capital. The exemptions are those which are limited by guarantee. The share capital is purchased by or is given to persons or other businesses who wish to own whole or part of that company.
The proportion of a company which an individual shareholder owns is dependant upon the percentage of the total issued share capital which they own.
For example, if a company has 100 £1 shares in issue (a total share capital of £100) and one individual owns 50 of these shares, then they would be deemed to have ownership of 50% of that company.
It is possible for shareholders to be people or other companies. That is, it is possible for an incorporated business B to own shares in company A.
The Companies Act however prohibits companies from being a shareholder of their own equity, meaning that company A can not own shares in company A.