My tuppence worth....
I think what might not be becoming clear to messrs anorton and macweenie yet, is the notion that all of the voltage across the LED and its resistor has to be accounted for: the 5v in the 5V---LED---1K(ohm)---Gnd scenario has to disappear by the time we get to the right hand end.
So here's how it all hangs together....
1) What's the input voltage? We're saying 5v, so we have that.
2) What's the voltage we must account for over the LED? Manufacturer will tell us, let's go with the 2.2V mentioned earlier
3) So what voltage must we disappear over the resistor? We started with 5, accounted for 2.2, so we have 2.8 left to drop over the resistor
4) How are we doing with Ohm's Law for the resistor so far? Well we don't know R, that's what we need to calculate; we do know the voltage (2.8v); we don't know the current....
5) But we do know that in a series circuit like this, the current through the LED has to go through the resistor: there's no other path. And we do know (or manufacturer will tell us) that it's 20mA, or 0.020A... this is the value to which we need to limit the current, the object of the exercise.
6) So now we can apply Herr Ohm to the resistor with R=V/I giving R=2.8/0.02 = 140 Ohm
This is all a consequence of Kirchoff's Voltage Law which Wikipedia
The algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.
The products of the resistances of the conductors and the currents is simply the voltages (Ohm's Law).
Do we have a loop though? The 5V---LED---1K(ohm)---Gnd doesn't look like a loop... but it is if you think of the 5v and Gnd being eg the two terminals on a battery... then it would look like a loop: 5V---LED---1K(ohm)---Gnd---Battery---5v
So now we can see Kirchoff's Voltage Law at work in our simple circuit...
1) Total EMF available in loop: 5V
2) Sum of the voltages in the loop: Vled
= 2.2 + Vresistor
3) So 5 = 2.2 + Vresistor
= 5 - 2.2
Does that help?