Ever see a tool like this one?

It's a torque wrench.  You use it like any socket wrench, but it tells you how tight you are tightening something.  You grab the black handle, and as you pull the black
number scale moves too.  The silver pointer stays still, so you can read how much torque you are putting on the nut (or whatever).

So what is Torque? It's a force applied about an axis.

How do you find it and what unit is it measured in?  If you apply a torque at 90°, the formula is t= rF.   The unit of torque must be meters*Newtons, usually seen in texts as N·m.  If you can't pull or push at exactly 90°, then you are wasting some of your force.
Have you already guessed that this involves vecors?  If you apply force at an angle, your useful force corresponds to the opposite side of a triangle, so the modified torque equation becomes t= rFsinq

At 90°, you apply 40N of force to a lever that is .5m long.  How much torque exists?
t= rFsinq = .5*40*sin90 = 20 N·m

What if the lever is in a hard to reach spot, so you have to apply your 40N at 45°?

t= rFsinq = .5*40*sin45 = 14.1 N·m

Here is an applet that you can use to manipulate the angle and strength of an applied force to see how torque changes. http://www.nadn.navy.mil/MathDept/mdm/wrench/wrench.html