Analog pins are the ADC (analog to digital converter) input pins. They are used for reading analog voltage (between 0-5V on arduino, by default). Check out the sample program for analogRead() command.
Digital pins are used mainly as output pins. You can connect various devices (LEDs, buzzer, LCD) on the digital pins and turn them on/off by writing HIGH or LOW on the respective pins. Check out digitalWrite() command. Before using a digital pin, you have to set it in input/output mode using pinMode() command. You can use a digital pin in input mode as well, especially when using interrupts in your code. Digital pins 2 and 3 of UNO can be used for interrupt detection. In general, you can check the status (on or off) of a device (or a switch) connected to a digital pin by using that pin in input mode. The command used is digitalRead().