Each mission has a preset primary objective completion timer, known as a turn goal i.e. you are challenged to complete the mission within X turns to be considered competent. (X = 15 or any even number from 6-32 inclusive). In some cases the mission will automatically end upon reaching the turn goal, such as Patrol Route, as the objective is to hold an area long enough for information to be gathered or for reinforcements to arrive. Sometimes a certain number of turns must pass before an event that will allow you to complete the mission is triggered. In this case it will be hard to do significantly better than the turn goal.
If you can complete the mission before or by the time the turn goal is reached, you will receive bonus as outlined in Mission Rewards.
If you go over the turn goal you will not automatically fail the mission but will receive no reward for your speed. There is an exception relating to your playing speed causing a mission failure, as 1 mission has a second timer that has a slow 5 count. In that mission reaching 5 will cause an automatic mission failure.