As far as I know there is nothing significant about Tyburn, most likely it was used as a place of execution from early on and as London grew it was never replaced and as the amount of crimes for which you could be hanged increased it saw more and more business. It helped though it was in a reasonably open space, during it's heyday executions were popular and would attract big crowds, so they needed somewhere that could accommodate several thousand people. As it was on the outskirts of the city perhaps it served as a warning to anyone entering what would happen if they got involved in crime.
It's believed that the expression to "go west" or die derives from Tyburn. Prisoners were kept at Newgate Prison (on the site of the Old Bailey) and then paraded through the city to Tyburn in the west of London to be executed. To "go west" therefore meant going to your execution.
