I always thought a potentiometer controlled current instead of voltage.
But in a tutorial for the Arduino it said that a potentiometer controls the voltage to the Arduino.
I hope someone can explain! 
A potentiometer controls it's resistance ratio only, Ohm's law will handle the rest and is dependent on the source voltage wired to the pot and the load resistance wired to the wiper in a DC circuit.
Lefty
As Retrolefty said, the potentiometer varies resistance only.
But by Ohm's Law, as the resistance goes down, the current thru the pot goes up. As the resistance goes up, the current thru the pot goes down. Voltage across the pot depends on the rest of the circuit.
The original Statement is valid.
"the potentiometer controls the voltage to the Arduino"
In the tutorial, you are hooking the resistive element of the potentiometer across ground and VCC rails.
The wiper is then connected to your input.
You sir, now have a voltage divider. Current will remain a constant, (Whatever the value of the pot is) and it is the ratio of voltage relative from each rail to the wiper that changes.
http://arduino.cc/en/Tutorial/AnalogInput
By turning the shaft of the potentiometer, we change the amount of resistence on either side of the wiper which is connected to the center pin of the potentiometer. This changes the relative "closeness" of that pin to 5 volts and ground, giving us a different analog input. When the shaft is turned all the way in one direction, there are 0 volts going to the pin, and we read 0. When the shaft is turned all the way in the other direction, there are 5 volts going to the pin and we read 1023. In between, analogRead() returns a number between 0 and 1023 that is proportional to the amount of voltage being applied to the pin.
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But doesn't a voltage divider require 2 resistors lol?
That is what the wiper on the potentiometer is giving you.
A rheostat gives you a variable resistance from one point to the wiper, but a potentiometer's wiper provides the variable resistance in two different directions simultaneously.
From the Ground to the wiper will be one resistance, and from VCC to the wiper will be a different resistance (Unless you are perfectly centered)- Thus providing your voltage divider.
First Line 
A potentiometer is a three-terminal resistor with a sliding contact that forms an adjustable voltage divider.
Well...
A potentiometer is equivalent to two variable resistors in series, with a constant total resistance and a variable proportion. The connection point (the middle pin) has a voltage between the voltage levels applied to the end of the POT (commonly a GND and a Vcc, but not always).
Since the total resistance of the POT is fixed the current is dependent on the total voltage applied to the POT, in cases like the demo the voltage is constant too (by design), so the current is constant, unless there is comparable drain on the 'middle' pin.
POT is normally used to provide a reference voltage, which is MEASURED between the middle pin of the POT and either end pin (commonly the one connected to GND).
Another method is to use the POT in series with a fixed resistance to provide CURRENT control.
Ah ofcourse! I'll search up some more info about voltage dividers.
Thanks for all the replies though!
This is my first post so excuse my explanation if its a bit too sloppy.
The answer to you question is "both depending on how the component is wired".
If you wish to understand how a potentiomenter also called a pot works try taking a breadboard and wiring several resistors 1Kohm in series. Like a voltage divider but with several resistors instead of two. Apply 5V across this series combination and then measure the voltages between, the negative of the power source and the points between resistors. You should see how the voltage changes. The voltage divides proportionally across all the resistors. Why is this? Because of ohms law that is. When you apply the 5 volts, current flows through all of the resistors in series and a volt drop occurs across each one. What you are measuring is the sum of the volt drops at different points in this chain of resistors.
Now remember any resistor can be modelled as a sum of resistances in series. For example a 10K resistor is technically the same as 10 1K resistors in series. Now imagine you took a piece of carbon or graphite like a pencil and took the graphite rod out. That length graphite rod is a resistor. If you take an ohm meter and measure you will see the resistance halfway down the length is approximately half the total resistance of the full length. If you measure a quarter of the piece of graphite you fill find the resistance a quareter of the full length. You could keep measuring like this ad infinitum and you will eventually realise that you can think of this graphite rod as being made up of millions of tiny resistances in series.
If you apply a voltage a current flows causing volt drops across all these resistors. If you then take a voltmeter and measure between one end and the mid point you will get half the supply voltage. If you measure between one end and a quarter of the way up from that end you get a quarter of the supply voltage. If you slide the one voltmeter probe up and down the graphite rod, while keeping the other probe on one end you will see the voltage varies and gets bigger as you move the probe further from the end where the other probe is. You now a crude potentiometer. The wiper slides up and down the graphite rod which is connected to the power supply.
If you can get those non multiturn trim pots I suggest you try and break one open and you will see a graphite track with the wiper moving across the track.
So you can think of a pot as a variable voltage divider of sorts.
If you want to control current you need a variable resistor or rheostat, a pot can also be used as a rheostat by only using two of the terminals. You use the wiper and one of the other terminals. I leave this for you to think about.
Pots are often used in microcontroller circuits as a simple way of obtaining an analog voltage. If in other circuits pots are actually used for this purpose. There are limitations such as being careful not to load them too much, but nothing you have to worry about when using Arduino