A couple of things: First, like the commenter @Artem S. Tashkinov says, (in some shells) the export PATH needs to be on a new line since it's a separate command. It's saying set the new PATH as an environment variable. An environment variable is a variable (a dynamic value) which is used not only by one program, but the whole environment. As a simplification, think environment = shell (corrected thanks to ilkkachu).
Secondly, to more directly answer your question, $PATH is an environment variable which stores the locations of executables (programs). You are simply appending /usr/local/openmpi-3.0.0/bin to $PATH, so that if you type mpirun in a terminal, the shell knows it lives in /usr/local/openmpi-3.0.0/bin and can run it. The part before the colon is the contents of $PATH already; the colon means 'append what follows to what preceded'; and the /usr/local/openmpi-3.0.0/bin is the thing to append.
You may ask, why do I need the dollar? The simple answer is that the shell references variables that have already been defined with a $. For example, if I run:
NAME='BOB'
echo $NAME
the shell would print BOB, whereas
echo NAME
would result in the shell printing NAME.
Finally, you don't want to just change $PATH to the home of your executable (as opposed to appending), otherwise the system wouldn't know where other programs live.