What are the exact meanings of roll, pitch and yaw?
It depends somewhat on whether you are speaking from a pilot's point of view or from an engineer's point of view. Your reference to yaw, pitch, and roll ANGLES is indicates you are looking at the situation from an engineering point of view. A pilot would tend to think more in terms of yaw, pitch, and roll as expressing RATES of rotation, or in some cases as expressing angular (rotational) changes from the aircraft's PREVIOUS POSITION rather than from a prescribed starting reference position. If the desire is to express the aircraft's 3-dimensional position in space relative to the plane of the ground and relative to north, a pilot would tend to speak of heading, pitch ATTITUDE, and roll ATTITUDE (or bank angle). But read on for more.
But in the pitch = 90 degrees case I cannot easily understand how can
I think the roll.
When the pitch attitude is 90 degrees nose-up or nose-down, the yaw attitude (heading) and roll attitude (bank angle) become undefined, from the pilot's point of view.
(I've now found that this was also pointed out in this related answer which also has some other content that pertains to your question: What is the relation between roll angle and pitch angle? : )
This describes almost every possible attitude uniquely, unless the pitch angle is +/- 90 degrees. Then roll and yaw will become
Note that if you are banked (i.e. nonzero bank attitude or roll attitude, which ever you prefer to call it), then a motion that purely involves a nose-up pitch rotation and no yaw rotation or roll rotation will also increase the bank angle, and will also change the heading. Note also that a constant-banked climbing or descending turn (i.e. nose-up or nose-down pitch attitude) at a constant pitch attitude involves a roll rotation as well as pitch and yaw rotations. So, a pitch rotation is not exactly the same as a change in pitch attitude...and a lack of roll rotation does not always imply that the bank attitude (roll attitude) is not changing-- it's all a little complicated isn't it. Generally speaking, the rate of rotation about any given axis (pitch, yaw, or roll) is not the same as the rate of change of the pitch attitude, yaw attitude (heading), or roll attitude (bank angle), respectively. For example an aircraft pointing straight up can YAW through 180 degrees and end up pointing straight down-- it has changed pitch attitude with no pitch rotation.
Update to the question: I wonder whether any (yaw, pitch, roll) triple
set exactly describes the attitude/orientation of an aircraft or not.
So could you please tell me that can any orientation of a flying
object described with a unique y,p,r triplet?
In ALMOST all cases the answer is "yes". The exception, from the pilot's point of view, is when the nose is pointing straight up or straight down (i.e. the pitch attitude is plus or minus 90 degrees). In that case the yaw and roll attitude (heading and bank angle) become undefined and there is no easy way to distinguish between the aircraft's belly pointing north, south, east, or west, at least from the pilot's point of view. But read on for more on how an engineer would see the situation.
It has been noted that this can be resolved through the use of "quaternions". To learn more about that, you should probably ask another question.
Actually there is some need for refinement here. Taking off our "pilot's hat" and donning our engineer's "pocket protector"-- If we follow the CONVENTION given in this Wikipedia article on Euler angles https://en.wikipedia.org/wiki/Flight_dynamics_(fixed-wing_aircraft) , we note that if we START with an imaginary aircraft (this is a thought experiment, not an actual flight maneuver) in level flight with the nose pointing north, and THEN we rotate around the yaw axis by some prescribed yaw angle, FOLLOWED by a rotation around the pitch axis by some prescribed pitch angle, FOLLOWED by a rotation around the roll axis by some prescribed roll angle, we DO end up with the aircraft's position in space fully described. With this particular sequence of rotations, starting from wings-level flight pointing north, the angles that we've rotated about the yaw, pitch, and roll axes DO end up being exactly the same as the aircraft's heading, pitch attitude, and bank angle (roll attitude). Following this convention, the aircraft's three dimensional position in space CAN be fully described at all times with a yaw, pitch, roll "triplet"-- even including the directions that the canopy and the belly are facing when the aircraft is pointing straight up or straight down (pitch angles of 90 or -90 degrees). Note however that unless we arbitrarily REQUIRE the roll angle to be zero in the straight-up or straight-down cases, we notice that the straight-up and straight-down cases are not described by a UNIQUE set of yaw, pitch, and roll angles. For example, yaw, pitch, and roll angles of 90, 90, and 0 will give the same attitude in space as angles of 0, 90, and minus 90 -- in either case the aircraft is pointing straight up with its belly pointing east and its canopy pointing west. As another answer noted, the common thread is that in the nose straight-up or straight-down cases, the direction that the belly and canopy are pointing is tied to ( yaw angle minus roll angle) in the nose-straight-up case and ( roll angle minus yaw angle) in the nose-straight-down case. Therefore, any yaw-pitch-roll triplets that have a pitch angle of plus 90 degrees, and roll-minus-yaw equating to some given value, are describing the same orientation of the aircraft in space, including the direction that the canopy and belly are pointing.
For most pilots it is more intuitive to simply say that the heading and bank angle become undefined when the nose is pointing straight up or straight down, but the other method obviously has applications for defining the aircraft's attitude in space for engineering purposes.
Returning to a point already mentioned near the start of this answer-- sometimes with the words "pitch", "roll", and "yaw" it is not clear whether we are talking about a rotation rate, an attitude in space, or something else. For general pilot-speak, it seems a good rule of thumb to assume that these words refer either to rotation rates or to angles of rotation from the aircraft's previous position, unless it is very clear from context, or from additional attached words (e.g. "pitch ATTITUDE", or "pitched up TO 20 degrees") that they are being used to mean something else such as the aircraft's attitude with respect to the outside world. "Yaw" is the most squirrelly of the three-- we might sometimes say something like "we are going west but the nose is yawed 10 degrees right" to express a crab angle, or a sideslip angle-- i.e. the angle between the direction that the nose is pointing and something else, such as the direction of the ground track or the direction of the relative wind. (It wouldn't be clear which is meant from the above sentence, without further context.) It wouldn't be normal to say "the nose is yawed 40 degrees" to express a heading of 40 degrees, but in some particular contexts-- for example if we are working with "Euler angles" as described above-- a "yaw attitude" or "yaw angle" of 40 degrees could indeed be taken to mean a heading of 40 degrees. In many cases it is much clearer to just say "heading" rather than "yaw", "yaw attitude", or "yaw angle", if that's what we mean. Likewise for "slip angle" and "crab angle"-- both of these phrases are much clearer than any phrase involving the word "yaw".
But again, if we are using the system of Euler angles as described above for engineering purposes, then we might reasonably assume that "yaw", "pitch", and "roll" may be used to denote the corresponding Euler angles with no further elaboration. This wouldn't be normal pilot-speak.
As noted in another answer, it appears that "Tait-Brian angles" is a more accurate, or at least more specific, name for what I have called "Euler angles" in this answer. See the wikipedia link given above for more. Also see other answers for many well-presented, valid points.