"Limited by shares" means that the company has shareholders, and that the liability of the shareholders to creditors of the company is limited to the capital originally invested, i.e. the nominal value of the shares and any premium paid in return for the issue of the shares by the company. A shareholder's personal assets are thereby protected in the event of the company's insolvency, but money invested in the company will be lost.
A limited company may be "private" or "public". A private limited company's disclosure requirements are lighter, but for this reason its shares may not be offered to the general public (and therefore cannot be traded on a public stock exchange). This is the major distinguishing feature between a private limited company and a public limited company. Most companies, particularly small companies, are private.