HARES? HOUNDS? ON-ON?
Hashing is based on an old children's game called "Hounds and Hares" where one person (the Hare) takes off and lays a trail, usually with flour.  After 10 or 15 minutes the rest of the group (the hounds) chase after the Hare ultimately trying to catch the person laying the trail.   To keep the pack from catching them the Hare puts a variety of "Hash Marks" on the ground to try and throw the pack off. 
So, the general idea of the group chasing the Hare is to find the "True Trail".  This is usually done by the faster hounds finding the trail and then marking it with something like chalk to let the slower runners where true trail is. Or by blowing whistles and shouting "ON-ON" to let the rest of the pack know where true trail actually is.
Now, here is the joy if you are not an especially fast runner. By the time the faster runners have found the trail, the slower runners are just hitting the marks and don't  have to run as far.  This ulitmately means that the faster runners are doing most of the work for the slower ones.  Generally (very loose word) this keeps the group in some kind group form.  Most trails aren't much longer than 2-4 miles and even on really long trails, a shortcut "hint" can be discovered if you are really nice to Hare before the run starts.  Walking trails are very often found at most runs.
Now, why should you toil for an hour or so running after a Hare? Why?  THE BEER CHECK!!  A beer check is where you get to stop pursuing the Hare in middle of the trail, relax, and have a beer before you head back out on trail again. Trails can have one, two even nine beer checks depending on how far ahead the Hare wants to get.
So what happens at the end of  this trail?