Even simpler...
Why do I care about thrust? Because thrust is what lifts the rocket. It must exceed the force of gravity on the rocket it make it go up. We recommend a 5-to-1 thrust-to-weight ratio for any rocket to ensure that it goes "up" and not "sideways." Make sense?
Why do I care about impulse? Because it determines how high the rocket will go (presuming that it is going "up"). As mentioned, impulse is the product of thrust times seconds. So, as Matt wrote, 50 Newtons for 1 second is an impulse of 50 Newton-seconds. But 50 Newtons for 3 seconds is 150 Newton-seconds. Got it? Obviously if you apply 50 Newtons of thrust for three times as long, then you are going to go much higher (not necessarily three times higher, but definitely higher).
Now, back to the thrust-to-weight ration. 5-to-1 means if your rocket weighs 5 pounds, you needs 25 pounds of thrust. But pounds are not Newtons, right? So you have to convert. It just so happens that one pound of thrust = 4.44822 Newtons. So, if I have a rocket that weighs five pounds (fully loaded with motor and parachute, ready to launch), then I need a minimum thrust of 22.2411425 Newtons (let's call it 23 Newtons).
With me so far? Good. So, an E30 (which has 30 Newtons of thrust) can safely list this rocket. So can an F40, and a G54.
(Quiz: could an E22 safely lift this rocket? Probably, but we were looking for a minimum of 23 Newtons, so we'll say no.)
Now, those letters in front of the thrust number indicate a range of total impulse. In simplest terms, an F will have twice as much total impulse as an E, and a G will have twice as much as an F. (Not hard and fast, as these are "ranges" and not "numbers.")
So, if I had my five-pound rocket, and I had the following three motors, which one would most likely go the highest?
F120, G80, H50
Did you say the H53? Then you are right, because it has a total impulse in the H range, which is twice the G range and four times the F range.
If you said the F120, because 120 > 80 > 53, then you failed, because those are the thrust numbers, not the impulse numbers.
If you have followed me, then you have probably realized that an H53 is a very long-burning motor, whereas an F120 is a very fast-burning motor. Let's look at the actual burn times and total impulse numbers.
The F120 burns at 120 Newtons of thrust for 0.45 seconds, which produces a total impulse of 56.0 N-s.
The G80 (the CTI one, not the AT SU) burns at 80 Newtons of thrust for 1.15 seconds, which produces a total impulse of 92.9 N-s.
The H53 burns at 53 Newtons of thrust for 4.44 seconds, which produces a total impulse of 234.2 N-s.
This is all WAY oversimplified, but gives you the basics. Be careful of the pitfall of thinking that if it flew on an F, then it will fly on a G. Impulse does not determine safe liftoff weight -- that is thrust. So, just because an F40 will lift a rocket safely, it doesn't mean that a G20 will lift it. But if both motors can safely lift it, then the G20 will go twice as high as the F40.
Fire away with questions.