Here is a very good definition I just found:
from rec.guns... Most civilian rifle triggers are single stage. When you place your finger on it and apply pressure, the trigger shouldn't move at all, until it "breaks" and the gun fires. If it does move, it's called "take-up", and usually considered a Bad Thing.
Actually, what you lable as "take-up" in the above para, is called creep, and trigger "creep" is what is considered a "bad thing." Take-up is all together another phenom.
So let's understand the differences between "take-up" and "creep." Take-up is a wonderfully replicated feeling/action, found in 2 stage triggers, in preparation of firing, and creep is when you think you are trying to fire, but you just seem to keep pulling the trigger & it does not break cleanly. Creep is found in both single & double stage triggers.
Now, why do those who have experienced a good 2 stage trigger want a 2 stage trigger?
First, gas guns require a far greater pull weight than bolt guns, to be safe/legal for competition. So, when you must have a 4.5 lbs trigger, it's nice to split the weight between 2 stages, instead of one!
Second, many want a relatively heavy trigger for defense/law enforcement applications.
Third, there is a certain confidence in a 2 stage trigger. You pull through the first stage, and when you get to the "stop", you know you are on the ragged edge, and any movement of the trigger will fire the rifle. This is so in a match 2 stage trigger.
--Clint McKee