Each of these stats have many different applications.
Agility is the ability to be fast. If you're agile, you'll be able to get good
[INI] rolls, which decide the order of attack. They also come in handy with reaction rolls (
[DDG][BLK]), which help you prevent getting hit.
Dexterity is like agility as micro- is to macro-. If you have high dex, you'll be able to get extremely accurate hits in, which is the stat's main roll (
[ATK]). It also plays into the
[AIM] roll, as well as the
[STL] roll.
Strength is the ability to be, well, strong. Its main roll is the
[DMG] roll, where it adds to (could become multiply later) your damage on top of your weapon damage and accuracy, which all contribute.
Toughness is strength's counterpart, the ability to resist strength. Its main roll is in
[RST], and it's essentially your last resort for defense. Toughness will work exponentially, or at least polynomially, as it also makes up most of your HP, and as such will protect you much more at higher levels.
Endurance is something that isn't used too much, but it is very important in certain times. At 10 HP, every turn you must roll for
[DTH], where endurance counts for 60% of the roll, and can even prevent you from dying. As well, it's the most important roll for
[HP+].
As it's often said, "Knowing is half the battle." Intuition works based on the ability to deduce chances, being the most used stat by number of rolls. It's in all the reaction rolls, as well as all stealth-related rolls, and also anything that having logic can help with. This is the most influential stat, and also the one most saving stat.