What is an "alternative directory name" in CDPATH for the cd command?

The variable is not set by default (at least in the systems I am familiar with) but can be set to use a different directory to search for the target dir you gave cd. This is probably easier to illustrate with an example:

$ echo $CDPATH    ## CDPATH is not set

$ cd etc          ## fails: there is no "etc" directory here
bash: cd: etc: No such file or directory
$ CDPATH="/"      ##CDPATH is now set to /
$ cd etc          ## This now moves us to /etc
/etc

In other words, the default behavior for cd foo is "move into the directory named 'foo' which is a subdirectory of the current directory or of any other directory that is given in CDPATH". When CDPATH is not set, cd will only look in the current directory but, when it is set, it will also look for a match in any of the directories you set it to.

The colon is not used with cd, it is used to separate the directories you want to set in CDPATH:

CDPATH="/path/to/dir1:/path/to/dir2:/path/to/dirN"

In the manual, CDPATH is described this way:

The search path for the cd command. This is a colon-separated list of directories in which the shell looks for destination directories specified by the cd command. A sample value is ".:~:/usr".

For completeness, here is some experiment similar to terdon's.

$~> mkdir /tmp/2 ./2 ./3
$~> cd 2
$~/2> cd ..
$~> CDPATH=/tmp
$~> cd 2
/tmp/2
$~> cd ~
$~> cd 3
$~/3> 

As you can see, after setting CDPATH=/tmp, Bash looks in /tmp first for possible target directories. If not found in /tmp, it tries looking in the current directory. We could also note that (Shell Builtins)

If a non-empty directory name from CDPATH is used, or if - is the first argument, and the directory change is successful, the absolute pathname of the new working directory is written to the standard output.

I also want to share this:

$~> CDPATH=.:/tmp
$~> cd 2
/home/myuser/2
$~/2> cd 2
/tmp/2

In this continuation, CDPATH has been given two directories. The first is ., i.e., the current directory. Since it comes first, upon trying cd 2, we go to the /home/myuser/2, although /tmp/2 also exists. It is like $PATH, the first listed directories take precedence.