What does export PATH=something:$PATH mean?

What is this "export" phrase at the start?

export is a command (more precisely it's a Bash builtin, i.e. it's not an executable present in PATH, it's a command that Bash has built-in in itself).

Is it exporting the data to be available for Bash?

export sets the environment variable on the left side of the assignment to the value on the right side of the assignment; such environment variable is visible to the process that sets it and to all the subprocesses spawned in the same environment, i.e. in this case to the Bash instance that sources ~/.profile and to all the subprocesses spawned in the same environment (which may include e.g. also other shells, which will in turn be able to access it).

What is the first PATH and what is the second $PATH, and why do we need two?

The first PATH as explained above is the environment variable to be set using export.

Since PATH normally contains something when ~/.profile is sourced (by default it contains /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games), simply setting PATH to ~/.composer/vendor/bin would make PATH contain only ~/.composer/vendor/bin.

So since references to a variable in a command are replaced with (or "expanded" to) the variable's value by Bash at the time of the command's evaluation, :$PATH is put at the end of the value to be assigned to PATH so that PATH ends up containing ~/.composer/vendor/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games (i.e. what PATH contains already plus ~/.composer/vendor/bin: at the start).

https://help.ubuntu.com/community/EnvironmentVariables will probably help you. Also man bash may be very helpful with understanding how that works (at least in Bash)

Anyway - as for PATH= you're basically setting the PATH variable, adding some new paths to search through, adding at the end already / previously set paths, with $PATH (which is basically a reference to the PATH variable).

So, say your PATH was so far set to something like:

PATH="x:y:z"

and then you set

PATH="a:b:c:$PATH"

your PATH after that will be like:

a:b:c:x:y:z

I hope that makes sense.

And on top of that you export the new variable so it's known in your environment including also child processes / subshells.

Just be aware also that the order of the directories as set in PATH can be important. And something like PATH="$PATH:a:b:c" will give you the result:

x:y:z:a:b:c

which will affect the order of directories / paths while searching for a command (if you have your command in more than one of directories, the first found will be used - which may give you some unexpected results sometimes).

Here's the command so that everybody can follow along as they go through the bullet points. export PATH="~/.composer/vendor/bin:$PATH"

• export shell built-in (meaning there is no /bin/export ,it's a shell thing) command basically makes environment variables available to other programs called from bash ( see the linked question in Extra Reading ) and the subshells.
• Assignment in shell will take expansion first , then assignment will take place second. So what is inside double quotes gets expanded first, saved to PATH variable later.
• $PATH is the default PATH assignment ( or at least what the variable looks like up till this command appears in your .bashrc or .profile), and expand it.
• ~/.composer/vendor/bin is going to expand to /home/username/.composer/vendor/bin , where .composer is hidden folder due to the leading dot.
• That short ~/.composer/vendor/bin:$PATH have now transformed into long list of folders, separated by :. Everything is enclosed into double quotes so that we include folders with spaces in their path.
• Finally everything is stored into PATH variable and external commands allowed to use it

Simple Example

My interactive shell is actually mksh , which happens to also have export builtin. By using export to set VAR, my variable can be passed to and used by subsequent chain of commands/subprocesses, where I exported that same variable

$ echo $SHELL            
/bin/mksh
$ VAR="HelloAskUbuntu"
$ bash -c 'echo $VAR' 
$ export VAR="HelloAskUbuntu"                                                  
$ bash -c 'echo $VAR'                                                          
HelloAskUbuntu
$ 

Extra Reading

• What does “export” do in shell programming?