It is a clause which makes the transfer of shares subject to the prior approval of a corporate body, one or more shareholders or a third party. It prevents the company from being controlled by undesirable persons, for example by competitors or persons with a bad reputation.
This clause can be modulated, e.g. it can be provided that certain purchasers are automatically approved, e.g. the holding company of an existing shareholder.
This clause is often coupled with a pre-emption mechanism in order to allow shareholders who have refused the proposed purchaser to exercise a right of pre-emption over the shares.