You can use the digital inputs to read the status of a switch.
The analog inputs are for reading a voltage in the range 0 - 5V and return it as a number to your program. Use them to connect things like potentiometers or sensors.
The digital inputs can read high / low (0V OR 5V) there are 13 digital pins on the Arduino board. Use them to connect switches.
The only problem is that you can't use pin 0 and 1 if you also use serial communication (talk to your computer over the "USB" connection).
You could use the 4051 to (de)multiplex your digital i/O pins.