Using the western digital my passport essential as a home network backup?

today i purchased a western digital external harddrive(500 gb my passport essential) in hopes of being able to back up the computers on my home network. i know 500gb iis not alot, but the computers on my network dont have harddrives over 125 in size, and theres only 3. so is this possible for me to do? like to plug it into the back of my router and back up all of the files? thank you!