What is trimmed aircraft ?
Trimming is cutting out the control forces to zero. It is used in take off, cruise and landing (yes, all the time). In General aviation aircraft, this is achieved by an elevator and a trim tab combination. When the pilot push the controls, the elevator moves down creating an up force through the hinge and creates elevator hinge moment.
To keep this going with minimal or no inputs from the pilot, he adjusts the trim. In this situation, nose down trim is applied. This moves the trim tab up generating a down force. This force also acts through the elevator hinge. Once the tab moment and elevator moment becomes equal the aircraft will be in trim. That is zero stick force will be required to maintain the flight in the regime.
In Commercial airplanes things are a lot different. Because of their size a small trim tab is not going to be much of an use. But they also need a way to stay nicely trimmed. To achieve this, they have something called a Variable Incidence tailplane. As the name suggests, the pilot can vary the incidence angle of tailplane here. Still, the pilot to control the pitch pulls the elevator up or push it down. Let's look at an example. If the pilot wants to move up, he would move the elevator up. To trim the airplane the pilot now will have to apply nose up trim. As he does this, the tailplane will decrease its incidence via a jack screw. This is continued until the elevator and the tailplane are inline. This balances load from both surfaces which makes the stick forces zero.
How variable incidence tailplane works.
Some advantages of VI tailplane include a more powerful means of trim, can operate at higher ranges of CG and lower drag profile as less of the airplane is exposed to the air flow. One disadvantage is if the trim runs out of position, the airplane might go bonkers. As tailplane creates a much higher moment, there is no way the much smaller elevator can neutralise it. But there are mechanisms placed to avoid this.
One final point. Fly by wire aircraft have auto trim. So, Airbus pilots don't have to trim the airplane. It is done automatically by the computer.
In simple Understanding, The word Trimming is used at two places in an aircraft. One, which is not very common, is 'Fuel trimming'. This is done when pilot wants to reduce fuel flow for a given throttle setting to keep the EGT or TGT in control. But the most widely used application of trimming is in the flying control system.
When an aircraft flies level and steady, it is supposed to fly hands free. But in case there is some minor problem or maladjustment in the control system or disturbance of CG, the aircraft might deviate from its level flight automatically. For example it can fly left or right, it can fly one wing low or it can fly with a nose up or nose down attitude. So to keep it in level flight, the pilot need to hold the concerned control in opposite direction. (As per my example the rudder pedal or the aileron controls or the elevator controls). Don't you think this would be cumbersome for the pilot to hold a control continuously and fly for longer time. So there are trimmers available in every control system which can be operated by the pilot in desired direction and it will move the control to eliminate the error existing in that system rather trim the control and in turn the aircraft.
Trimming is done by moving a small control surface attached to the trailing edge of the main control surface known as trim tab. It can be moved by mechanical linkage or electrically. In many hydraulically operated controls, the complete control surface is moved slightly when trimmed.
Note***Please do not confuse Trim Tabs with Balance Tabs and Spring Balance Tabs. They look similar but their purpose is different.