Market orders are immediately filled at the National Best Bid and Offer (NBBO) price because the executing brokers are bound by U.S. Securities and Exchange Commission Regulation NMS. Keep in mind that once an order has been filled, it cannot be reversed.
Trading stocks with low volume may lead to partially filled orders. For example, when you make an order for 100 shares of XYZ, and there is a low trading volume for this particular stock, you may only get 50 shares at first. In this case, your order will remain open until the remaining shares are filled or if you cancel it. If the latter happens, you will keep the shares that were purchased.