A share is part ownership in a company. The number of shares you hold is a measure of how much of that company you own.
A share is one of a finite number of equal portions in the capital of a company, entitling the owner to a proportion of distributed, non-reinvested profits known as dividends and to a proportion of the value of the company in the case of liquidation of the company or sale of the shares.
Shareholders, also called 'members' and shareholders with voting rights, can vote on the major decisions of the company such as those taken at the company's Annual General Meeting (AGM).