Why do you need a second resistor when using a photoresistor/LDR?
The simple answer is that voltage is very easy for the Arduino to measure, while resistance is not, and most sensors such as Photoresistor (LDR), flex sensor, thermistors and more - are actually a variable resistors. 

The main reason it's hard to measure resistance changes is that the Arduino (and most IC) contain a tiny system called Analog to Digital Converter (ADC). This system translates changes in analog voltage to a series of 1's and 0's that can be in turn converted to an Integer for example. 

The ADC is designed to read voltage changes, and if we want to use the Arduino's analogRead (which utilizes the ADC) to get the Photoresistor readings for example, we will need a way to convert the changes in resistance to changes in voltage - and a voltage divider is the easiest way to do it. 

It is true that the sensor is already a resistor, and as such it should change the voltage across it. But you would have trouble measuring the voltage changes, since there is no reference point except for Vcc (5V) and Ground:



In contrary, when using a voltage divider, you have a well defined reference point to measure the voltage changes: