Several have touched on the ideas I learned in physics, so much of this is the previous ideas combined or re-stated, hope it helps.
cause many different motions on the aircraft, depending on where the aircraft strikes the air mass causing turbulence. In the case of relatively large air masses (compared to the size of the plane), in level flight the aircraft will experience a sharp increase (or decrease) in lift as the wings encounter more (or less) dense air. This is experienced like grabbing the wingtips and pulling them up or down (oversimplified, in general terms, for illustrative purposes- actually the forces act on the entire wing, but the effect is basically the same). I believe this is the most common kind of turbulence encountered, but if any more experienced (or pilots) have other views, I welcome them.
As previously stated, if the aircraft were a rigid body, the entire aircraft would pitch up and down exactly the same (ignoring pitch for now- assuming "level" flight) However, the aircraft body flexes much the same as the wings, so when the centre is almost instantly pushed up 2 feet by the wings, the wave of force takes time to travel through the body of the aircraft and changes according to (generally) two things: The flexibility of the material, and the distance from the origin. A flexible ("springy") material will absorb some of the force, and slow down the wave, whereas a rigid material will transfer the full force rapidly. Think of this like the difference between a cheerleader spinning a baton- rigid, fast, simultaneous motion- and a ribbon tied to the end of the baton. The flexible ribbon transmits the motion more slowly, so you have a visual reference of the force applied to the baton a few seconds ago. (ignore the air viscosity for now- you would see my point clearly in a vacuum, it would look a bit different on the ribbon tho-)
The second piece of this- distance from center- is also important, as Comorin
noted the aircraft body becomes a lever. As the wave of force slows down moving away from the origin, it also becomes "taller". If you take a flexible rod, like a plastic yard-stick (or meter-stick) and apply an oscillating up-and-down motion of 4 inches (10cm) to the center, you realize that you can make the ends flap up and down 12" (30cm) or more. As the wave travels away from the point of force, it seems to get taller (stronger), the lever effect, right? So if the center passengers are pushed up 2 feet and weigh 100 lbs., the force above the wings is 200 ft-lbs, but at the tail end of the plane, the body flexes and the passengers are thrown up 3 feet-so if we look at another sexy 100lb passenger, she gets 300 ft-lbs of force, right?
This is actually a misconception-- the lever is reversed in this example. To get the ends to move with that much force, you are actually applying a greater force to the center of the stick. If each end of the stick has 5 newtons of force accellerating the flexing of the yardstick so that the tips rise, then you are applying a little more than 10 newtons of force in a rising motion to the center of the stick.
So take the example and apply a set amount of force to the center. So you raise the center of the stick over a period of 1 second with 10 Newtons of force and it moves 3 inches. (But the ends don't move just yet-) The resistance (inflexibility) of the stick limits the distance of travel at the center. But a foot further away, the wave of force acts on a section of the stick that is already moving- because of the inflexibility of the material- and so after 1.5 seconds that section of the stick is being accelerated by the peak of the wave that took time to travel to that part of the stick. It is now just under 5 Newtons of force, having lost energy to friction- but the stick moves 6 inches.
The friction acts against the wave, taking it's energy and transforming it to heat. I really don't know with an aircraft body, but I suspect by observing the effects that the effect of friction is less than the effect of the flexibility- so as the wave travels it will move the front and back of the airplane more than the center, like in the stick example, but with less force. An object with more friction (less flexibility) will absorb more of the energy and move less- like a plexiglass pane. Given a long enough (or thick enough, but that's no fun to watch) plexiglass sheet, you could hit it in the center and the wave of force would die before it reached the edges- it has smaller oscillations as it moves away from the point of impact.
So as the same wave of force travels through the stick, it accelerates the material just a little further. So by the end of the stick, the peak of the wave is 12". But with much less
force per distance traveled. At the origin, a force of 5 newtons moved the stick 3 inches- (or the force of turbulence bounced the passengers 2 feet. Strong force acting against stationary metal and passengers and rapidly accelerating them for a short time and distance. Relatively high "G-force") By the time the force reaches the end of the stick, a somewhat slower wave with slightly less energy moves the already moving tail end to a peak of 12". (Or a slightly
less powerful wave moves the tail of the aircraft three feet. Nearly the same force acting against an already moving aircraft frame, taking slightly longer to accellerate the passengers. Slightly lower "G-force".)
So the passengers of a non-moving aircraft suspended in the sky at the center of lift suddenly take a force applied at the center of lift. The passengers at the center experience a sharp force for a short time, a "jarring" motion. The passengers at the nose and tail experience a slightly less sharp force for a slightly longer time, a "rocking" motion. In a mile long aircraft, the passengers at the nose would experience a smooth flop, like a baby in the treetop. (except that the frame would fail and they'd all be falling without lift and with minimal turbulence...)
Now as to pitch, roll and yaw, as explained by Comorin
earlier, those will depend on the distance from the force applied- with very little difference in perception of roll, more in pitch. As to why more turbulence in the back? Because of turbulence on the horizontal stabilizers on the tail. Hardly noticed in the front, except as change in pitch. But the back of the plane can jump 2-3 feet without the pilot's knowing the difference.
In the case of T-tails, the pitching force on the stabilizer is applied to a place actually behind the body of the airplane, so the rotational force is greater- I always wondered, but it seemed top me that the DC-9s and 727s were turbulence hogs, while the 737s and A320s just skipped on the clouds.
Sorry for the verbose response, I hope someone out there likes my prose, just blowing some steam after work....