Fargo,
Boolean varibales are variables that are either true or false. They are not numeric values, or string values (alpha characters). The are used often with if - then statements. Here is an axample:
If (getDamage _soldier < .4) then {_soldierhealthy = true} else {_soldierhealthy = false}
When you use a boolean on the "if" side of the if - then you do not use any == signs or >=, instead you just state the varialbe for a positive check, or "not" in front of the varible for a negative check like so:
If (_soldierheathy) then .......
or
If (not _soldierheathy) then .......
For short you can use "!" instead of "not" also you can use "?" instead of "if" and ":" instead of "then". I hope this helps. If you want you can examine some of the scripts in the editior depot. Almost all scripts of any advanced level will make use of boolean variables (true or false conditions). If you look at these scripts you can see how they are used and some examples of the situations where they are usefull.