1/508th PIR in close-to-English is:
First Battalion, 508th Parachute Infantry Regiment, which was one of the units of the 173rd Airborne Brigade stationed in Italy, now with the 82nd Airborne Division in North Carolina.
Just so happens to be the same unit Sergeant Brian Horn was in, the guy who started the idea of Any Soldier.
In the Army, unit sizes go (smallest to largest):
Team - Squad - Platoon - Company - Battalion - Brigade - Division - Corps
There are other 'in between' sizes specific to special groups but the above is pretty much the standard.
Now, how big are each of the above? Again, depends on the type of unit. A Division is the same as a medium city.
Confusing? Yes, but that helps confuse the enemy....and us ;)