The number of authorized shares is the total number of shares your company is allowed to issue to its founders, investors, and employees. It is indicated in the Articles of Organization or the so-called Certificate of Incorporation.
The number of authorized shares suggested to start a company within the technology industry based on common practice is 10,000,000 so that shares can be issued to future investors. This way it is less likely that the client will need to amend the Certificate of Incorporation, which has an additional cost, to increase the amount of the authorized shares in order to follow their company’s growth.
When you allocate part of the authorized shares to a founder, investor, or employee it means that the shares are issued to a stakeholder/shareholder. The way you allocate your company's shares will be reflected in your Post-Incorporation documents and this can be changed later.
Normally companies reserve a number of shares to the founders or a parent company upon the corporation, which means the ownership is granted to the founders. At the same time, a small part of the authorized amount keeps available for issuance to be used in the Equity Plan or in restricted stocks. The company can also issue preferred shares during a financing round (this is when they raise money for their corporation) and add the authorized amount for these ones in the Articles of Incorporation (Certificate of Incorporation).
The shares to the founders are normally common and restricted stocks. The stockholders need to pay a nominal (par) value set up as indicated in the Certificate of Incorporation to the corporation for purchasing the shares. These shares can be bought back by the company in case one of the founders leave the company. Shares mean ownership so if the owners want to transfer their shares to other stakeholders they can do so, partially or entirely, and get paid for the shares.