An order is filled when it matches against the other side. A market-order fills immediately at whatever prices are available. A limit-order fills only if price reaches it, and may fill partially if there is not enough size at that level.
Fill quality (the price relative to the quote at the time) is how execution is measured. Each fill prints on time-and-sales.
Example: you place a limit buy for 500 shares at $30.00. Only 200 shares trade at that price before the stock moves up. You have a partial fill of 200 and 300 still working.
Related: market-order, limit-order, slippage, time-and-sales