Which variable defines the directories in which a bash shell searches for executable commands?

The PATH variable is essential in a bash shell as it specifies the directories that the shell searches through to locate executable commands. When a command is entered, the shell looks for that command in the directories listed in the PATH variable in the order they appear. If the command exists in one of those directories, it executes it; if not, it returns an error indicating that the command was not found.

Other environment variables like HOME, PWD, and USER serve different purposes. HOME signifies the current user's home directory, PWD denotes the present working directory, and USER shows the username of the current logged-in user. While these variables provide helpful information about the user's environment, they do not affect the command search process that is significantly governed by the PATH variable. This distinction clarifies why PATH is the right choice when considering which variable defines where the shell looks for executable files.