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The meanning is shown in the definition of sesor_msgs/CameraInfo.msg in ros API:
P is needed in this type of msg.

Projection/camera matrix
[fx' 0 cx' Tx]
P = [ 0 fy' cy' Ty]
[ 0 0 1 0]
By convention, this matrix specifies the intrinsic (camera) matrix
of the processed (rectified) image. That is, the left 3x3 portion
is the normal camera intrinsic matrix for the rectified image.
It projects 3D points in the camera coordinate frame to 2D pixel
coordinates using the focal lengths (fx', fy') and principal point
(cx', cy') - these may differ from the values in K.
For monocular cameras, Tx = Ty = 0. Normally, monocular cameras will
also have R = the identity and P[1:3,1:3] = K.
For a stereo pair, the fourth column [Tx Ty 0]' is related to the
position of the optical center of the second camera in the first
camera's frame. We assume Tz = 0 so both cameras are in the same
stereo image plane. The first camera always has Tx = Ty = 0. For
the right (second) camera of a horizontal stereo pair, Ty = 0 and
Tx = -fx' * B, where B is the baseline between the cameras.
Given a 3D point [X Y Z]', the projection (x, y) of the point onto
the rectified image is given by:
[u v w]' = P * [X Y Z 1]'
x = u / w
y = v / w
This holds for both images of a stereo pair.

It says in monocamera, for rectified image, P is [K | 0]; for raw image P is [K' | 0], the parameter of K' may differ from K, which can be thought as computed by projecting 3D points to rectified images. I guess K' is computed from projecting 3D points to raw images!