How does an AND gate behave in this situation?
The AND gate has a truth table that looks like this:   

Input A  |  Input B  | Output
   0     |     0     |    0 
   0     |     1     |    0 
   1     |     0     |    0 
   1     |     1     |    1


So when both switches are on the output will be high. This circuit could be designed better for example using a resistor to limit the current flowing through the Light Emitting Diode (LED), and tying the inputs to either V+ or ground. So that you get more reliable operation. 

An example would look like this: 







simulate this circuit &ndash; Schematic created using CircuitLab