The owners of a company may want additional capital to invest in new projects. They may also simply wish to reduce their holding, freeing up capital for their own private use. By selling shares they can sell part or all of the company to many part-owners. The purchase of one share entitles the owner of that share to literally share in the ownership of the company, a fraction of the decision-making power, and potentially a fraction of the profits, which the company may issue as dividends.
In the common case, where there are thousands of shareholders, it is impractical to have all of them making the daily decisions required in the running of a company. Thus, the shareholders will use their shares as votes in the election of BoD members.
Each share constitutes one vote (except in a cooperative society where every member gets one vote regardless of the number of shares they hold). Effective control rests with the majority shareholder (or shareholders acting in concert).