Civil aircraft are aerodynamically stable
They inherently want to fly in a straight line. Moving the stick out of center position is telling it to do something other than that.
So if the airplane isn't going in a straight line, the first place you look is the pilot doing something with the stick. If the pilot simply lets go, aerodynamic forces should push the stick to center, and make the aircraft fly straight.
Why a pilot can go wrong with the stick
Trying to actively use the stick to command the aircraft to fly straight, has a problem. It takes time for the aircraft to respond to controls - the bigger the aircraft, the longer the time*. This can cause pilot-induced oscillations -- imagine a microburst pushes the tail down, raising the nose, and instantly the plane returns to normal air -- the plane starts to self-correct (pushing the nose back down) and the pilot commands this also. Two seconds later, both have effect, and now the nose is too low. So the pilot pulls back to raise the nose - rinse, wash, repeat, in other words, the pilot is causing the problem by trying to fix it, because his control inputs are too much or too late.
So it can be useful for the pilot to stop doing that, let go, and let the natural stability do its job. This won't fix every possible upset, but will fix many.
This bounced landing was caused by pilot induced oscillations. Again the watch word is "stop doing that", but in this case it's expanded to "stop trying to land, and give appropriate inputs to take off again and go-around".
The asterisk: Trims
The pilot has controls to decide exactly what "straight line" means. These are trim controls, which allow fine-tuning adjustments to the elevator and rudder. For instance when an airplane is climbing to altitude, the pilot doesn't pull the stick back the whole time. She adjusts the elevator trim so that "straight line" means the desired rate of climb. Now she doesn't have to hold the stick at all.
She can also trim the rudder to compensate for imbalance or differential thrust; typically you trim to fly in a straight line, but she could trim to fly in a lazy circle if she really wanted to. (why??)
The elevator trim setting varies somewhat on every flight, due to differences in weight and balance front-to-back. (aft balance requires more nose-down trim, and heavy weight requires more nose-up trim so the wings have higher lift). Trim also changes during the flight due to fuel burn-up or people moving around.
* Using the stick to push the elevator up doesn't actually nose up the aircraft - air passing the elevator starts to push the tail down, and after a second or two, the tail goes down and the nose up.