What is a capital X in posix / chmod?
The manpage says:
execute/search only if the file is a directory or already has execute permission for some user (
X)
POSIX says:
The perm symbol X shall represent the execute/search portion of the file mode bits if the file is a directory or if the current (unmodified) file mode bits have at least one of the execute bits (S_IXUSR, S_IXGRP, or S_IXOTH) set. It shall be ignored if the file is not a directory and none of the execute bits are set in the current file mode bits.
This is a conditional permission flag: chmod looks at whatever it is currently processing, and if it’s a directory, or if it has any execute bit set in its current permissions (owner, group or other), it acts as if the requested permission was x, otherwise it ignores it. The condition is verified at the time chmod applies the specific X instruction, so you can clear execute bits in the same run with a-x,a=rwX to only set the executable bit on directories.
You can see whether a file has an execute bit set by looking at the “access” part of stat’s output, or the first column of ls -l. Execute bits are represented by x. -rwxr-xr-x is common for executables and indicates that the executable bit is set for the owner, group and other users; -rw-r--r-- is common for other files and indicates that the executable bit is not set (but the read bit is set for everyone, and the write bit for the owner). See Understanding UNIX permissions and their attributes which has much more detail.
Thus in your example, u=rwX sets the owner permissions to read and write in all cases, and for directories and executable files, execute; likewise for group (g=rX) and other (o=rX), read, and execute for directories and executable files.
The intent of this operator is to allow the user to give chmod a variety of files and directories, and get the correct execute permissions (assuming none of the files had an invalid execute bit set). It avoids having to distinguish between files and directories (as in the traditional find . -type f -exec chmod 644 {} + and find . -type d -exec chmod 755 {} + commands), and attempts to deal with executables in a sensible way.
(Note that macOS chmod apparently only supports X for + operations.)
From the man chmod :
The letters rwxXst select file mode bits for the affected users: read (r), write (w), execute (or search for directories) (x), execute/search only if the file is a directory or already has execute permission for some user (X), set user or group ID on execution (s), restricted deletion flag or sticky bit (t).
(emphasis mine).
However that doesn't clarify it very much. This article has the two rules that clarify what it does:
For example, we issue the following chmod command on a directory:
# chmod -R u=rwX,g=rX,o=rX testdir/`
Using the uppercase X, the above command sets the executable attribute according to the following two rules:
If the file is a directory, then it sets the executable attribute for the owner, group and world, which means that they can enter this directory.
If the file is a regular file, then it will add the executable attribute to its permissions, if the file already has some execute bit set. If the file has no execute bit set, none will be added.
Using the lowercase x it would be impossible to achieve this result with one command only.
Hope that clarify the use of X.