Oh, life used to be so simple. In the good old days, we had this thing called "gyroscopic precession" and we used that term to describe how you had to put the pitch-change in back *here* to get the rotorblades to react up *there*. We said that the rotor's largest displacement happened "90 degrees" beyond the point at which we made the control input. We had all played with gyroscopes as children, so this simple analogy sufficed to explain how a helicopter rotor worked. It still does.
But then some egghead engineers came along and said, in effect, "Whoa, wait a minute."
In a "real" gyroscope, they say, the rotor is fixed solidly to the axle. And in a "real" gyroscope, the reaction actually is 90 degrees beyond where we put in the force. You can measure it, supposedly.
But helicopter blades are not fixed solidly to the mast. There are these things called flapping hinges. And even if there are no hinges per se, the blades are quite limber and act as a hinge. But remember, we're not just applying a force to the edge of the disk to cause it to tilt. We're changing the pitch of the individual blades themselves, causing them to fly up or down to a new position as they go 'round. Only they don't react instantaneously. This is where the term "phase angle" comes in. It's a term engineers invented to confuse pilots.
And so, okay, the precession is "not quite" 90 degrees, not exactly. It is something less (but it could be more). Nevermind, it does not matter. Those wacky engineers have figured out just how much "phase angle" they're dealing with, and they design and rig the cyclic controls so that when *you* push forward on the cyclic, the disk tilts down in front. Clever, eh? As a pilot, that's all we need to know.