Let's start with Ohm's law
E = I x R
E = voltage (electromotive force, measured in volts)
I = current (measured in amperes)
R = resistance (measured in ohms)
A resistor is a controlled way of applying a specified resistance to the current flow (from the classical thinking) in a circuit.
Ohm's law gets tricky around LEDs. In some respects, they almost look like a constant voltage source when you model them.
If, for example, you have an LED with a forward voltage drop of 2V and a 6V battery, and you want to limit the current through the LED to 0.1A
Then R = E / I = (6-2)/0.1 = 4/0.1 = 40
You would put a 40 ohm resistor in series with the LED.
This is a gross example to make the numbers work. If you took that resistor out, you would probably blow the LED.
Batteries have internal resistance (and it goes up as they are used up) which needs to be calculated as well.
So, removing the resistor will make the LED brighter--but may blow it out.
For example, the early versions of the Streamlight 4AA LEDs did not come with a big enough resistor, and putting lithium batteries in the light--with their lower internal resistance--caused some of these to fry.
I hope I helped.
Cheers,
Richard