What does adding PATH to .bashrc do?
When you run a command in bash (or any other Unix shell), the shell searches for this command in a number of directories. The list of directories is stored in the variable called PATH, paths are separated by :.

The command in question extends the already defined $PATH by two additional paths:


/usr/local/bin which is the usual place user-provided commands get installed to
The output of $(brew --prefix coreutils)/libexec/gnubin which points to some utility commands required by brew


To see the current value of PATH, run echo $PATH in Terminal.