I don't want to pretend to be any kind of expert on this subject, however the aerodynamic principles that are talked about with reference to phase lag and flapping to equality do seem fair enough to me.
Here's a shot at trying to describe what happens, for an anticlockwise when viewed from above rotor:
For a helicopter in the hover in nil wind, the pitch setting on the blades could be said to be the same, and lift equal, all the way round.
Let's say you want to tilt the disc forward to, funnily enough, fly forward.
You move the cyclic forwards. The pitch change system acts to make the pitch of the blades vary around the disc, with the maximum setting occurring on your left, and the minimum on your right. That means that from the rear of the disc, the blades experience less lift than they had in the hover and therefore start to fly down. The minimum pitch setting occurs on your right, so that's where the blades are flying down fastest - but they haven't finished heading downwards.
That doesn't happen until they get to the front of the disc, where they will again be at the original 'equilibrium' pitch setting.
From there, on the left side, they will start to fly up again, so you finish up with the disc tilted forwards like you wanted.
When the aircraft just starts to fly forwards, the left and right sides are producing the same amount of lift, so you are 'wings level'.
As you pick up speed, the advancing side gets more airspeed and the retreating side less, so the aircraft should roll, you'd think.
However, because we have flapping hinges and/or flexible blades, the advancing blade flaps upwards (decreasing it's angle of attack) and the retreating blade downwards (increasing it's angle of attack) until they are back at the original equilibrium between lift and centripetal force (or whatever the force is called that wants to throw them outwards!).
They have therefore 'flapped to equality' of lift, and the machine doesn't roll.
However, to achieve this, as we said, the advancing blade flaps up and the retreating blade down, with the maximum and minimum pitch angles respectively occurring at the left and right sides of the helicopter.
Lift is equal laterally, but the blade is flapping, with the maximum rate of flap at the sides.
As described above, however, the maximum extent of travel isn't reached until 90 degrees later; i.e. the blade would be flapping down fastest on our left, reaching its lowest point at the back, relatively speaking (bearing in mind it's already been pushed forward in the first place).
This is the phenomenon of flapback, meaning we now have to push more forward cyclic than we would have otherwise to keep going forward.
No gyroscopics required! That's not to say no gyroscopic forces are present, but I think aerodynamics explains things easily and adequately.
That's quite enough of a post for now, my brain hurts.