Defining a variable with or without export

export makes the variable available to sub-processes.

That is,

export name=value

means that the variable name is available to any process you run from that shell process. If you want a process to make use of this variable, use export, and run the process from that shell.

name=value

means the variable scope is restricted to the shell, and is not available to any other process. You would use this for (say) loop variables, temporary variables etc.

It's important to note that exporting a variable doesn't make it available to parent processes. That is, specifying and exporting a variable in a spawned process doesn't make it available in the process that launched it.

To illustrate what the other answers are saying:

$ foo="Hello, World"
$ echo $foo
Hello, World
$ bar="Goodbye"
$ export foo
$ bash
bash-3.2$ echo $foo
Hello, World
bash-3.2$ echo $bar

bash-3.2$ 

Others have answered that export makes the variable available to subshells, and that is correct but merely a side effect. When you export a variable, it puts that variable in the environment of the current shell (ie the shell calls putenv(3) or setenv(3)).
The environment of a process is inherited across exec, making the variable visible in subshells.

Edit (with 5 year's perspective): this is a silly answer. The purpose of 'export' is to make variables "be in the environment of subsequently executed commands", whether those commands be subshells or subprocesses. A naive implementation would be to simply put the variable in the environment of the shell, but this would make it impossible to implement export -p.

It has been said that it's not necessary to export in bash when spawning subshells, while others said the exact opposite. It is important to note the difference between subshells (those that are created by (), ``, $() or loops) and subprocesses (processes that are invoked by name, for example a literal bash appearing in your script).

• Subshells will have access to all variables from the parent, regardless of their exported state.
• Subprocesses will only see the exported variables.

What is common in these two constructs is that neither can pass variables back to the parent shell.

$ noexport=noexport; export export=export; (echo subshell: $noexport $export; subshell=subshell); bash -c 'echo subprocess: $noexport $export; subprocess=subprocess'; echo parent: $subshell $subprocess
subshell: noexport export
subprocess: export
parent:

There is one more source of confusion: some think that 'forked' subprocesses are the ones that don't see non-exported variables. Usually fork()s are immediately followed by exec()s, and that's why it would seem that the fork() is the thing to look for, while in fact it's the exec(). You can run commands without fork()ing first with the exec command, and processes started by this method will also have no access to unexported variables:

$ noexport=noexport; export export=export; exec bash -c 'echo execd process: $noexport $export; execd=execd'; echo parent: $execd
execd process: export

Note that we don't see the parent: line this time, because we have replaced the parent shell with the exec command, so there's nothing left to execute that command.