Manny,
Here's another way to look at it:
Looking at it from the prototype (real trains) -- 1/48 means 48 times smaller than the real thing. It's in feet. 1 foot on your layout equals 48 feet in the real world.
Looking at it from the model (O scale trains) -- 1/4 means that one foot in the real world occupies 1/4" on your layout. It's in inches.
The arithmetic (tying both together) -- 1/48 x 12 inches per foot = 1/4"
Mike