Analog signals are a variable voltages representing the brightness of the pixels, digital is the same but instead of a voltage, a numerical representation of it is sent instead.
CRT monitors used the voltage to directly control the intensity of the beams inside the tube but since LCD and OLED screens have become common which need computer control to address individual pixels, it has become easier to skip the video card conversion of brightness to analog then the monitors analog to brightness and instead connect the digital signal straight through. From a picture quality aspect, there is little if anything between them but using digital does eliminate some of the problems with the high voltages and wide bandwidths amplifiers needed in older CRT monitors. DVI-I and other systems carrying both types are there for compatibility and I would guess will be 'retired' as HDMI takes over.
Brian.