The analog inputs of the arduino can't read resistances. They read voltages and compare them with a reference voltage. They give you a number between 0 and 1023 so the read voltage is 1/1024 of the reference voltage.
The configuration of the LDR and the resistor is called a voltage divider. It is needed to get a voltage that the analog pin can read.
The intersection of the LDR and the resistor is where you can measure that voltage (or connect it to the analog pin of the arduino).
More info about this subject was already given in this question:
Why do you need a second resistor when using a photoresistor/LDR?Why do you need a second resistor when using a photoresistor/LDR?
Wiki page about voltage dividers and the relevant formulas
