The Generation System something created for the purposes of tracking an individual's lineage, mainly by marking the purity of their blood from their dark elf progenitors. It serves the purpose of classifying individuals, and serves as a mark of respect, while also allowing those older drow who do not care to keep track of their ages a way to refer to themselves. In reality, referring to one's self in generation terms only measures how many times removed from a dark elf ancestor one is, and is not a viable basis for gauging age. As the society is matrilinear the mother's lineage is the one which counts.
For example: If a Second Generation woman has a six-hundred year old daughter, and gives birth to another girl within the past year, both are Third Generation regardless of the age difference. Thus, most younger drow still track age and it isn't until they lose interest in watching years that they switch to the generation system.
A First Generation is a dark elf that is living in the underworld. Because they were born prior to coming to the underworld, they are still full-blooded dark elves and have the dark elf coloring. Subsequent generations look more and more drow-like the farther removed from the dark elves they get, which results in a general washing out of prominent features, such as hair or eye colors. While a tenth generation might have some hint of color to their hair, the third generation may also show signs of developing white hairs.