Genealogists are often asked: "Why do you spend so much time with dead people?" Rabbi Adin Steinsaltz, in his book Teshuvah: A Guide for the Newly Observant Jew gives a better answer than I ever could (p.60):
The search for roots, even in the simplest genealogical sense, is likely to be a meaningful experience on both the personal and religious levels. But it is important to pursue it even if the meaning is elusive. Lineage is not just a matter of empty self-congratulation. All lineage, and not just that of nobility, carries with it a certain responsibility. A great person discovered among one's ancestors is not just a cause for bragging but something that must be related to and learned from. The sense of kinship with such a figure can be a source of strength and encouragement to one suffering spiritual distress or self-doubt. It need not be a famous or distinguished figure; even a person---remembered or reconstructed---who was at one with himself and with the world can serve as an anchor point and source of commitment. Such connections represent, in a sense, a broadening of the commandment to "honor thy father and thy mother," a commandment described through the ages in terms of the obligation of the "branch" toward the "root" from which it sprang and that nourished it. Honor of parents and of earlier generations of forebears is connected, in turn, with kibbud ha-makom, honoring the source of all human life. Strengthening one's ties with one's own past is part of renewing one's connectedness with the sources of Jewish life in general.
Rabbi Shlomo Carlebach offered an alternative view, just as eloquent:
"It doesn't matter who your grandparents are. It matters who your
grandchildren are."
Here's a quote from Rabbi Berel Wien's commentary on Parshat Lech L'cha, November 6, 2003. In place of "Avraham" read "our ancestors" and you'll see the connection to genealogy as a means of reaching back through and honoring the generations:
Western society, post-modern and essentially rootless, pursuing pleasure and individual gratification at almost all cost, unwilling to sacrifice for the future or for others, suffers from a lack of heroes and role models. Sports stars, movie actors and actresses, princesses and politicians, all have proven to be poor objects of emulation and imitation. Having no standard by which to measure ourselves, we are unhappy in our narcissism and medioocrity. We do not realize the cost to ourselves and our world of remaining ignorant of Torah and Jewish tradition, of not attempting to reach out and touch the hem of our father Avraham, of being smug and self-righteous in our prosperity and selfishness. Having no memory any longer even of our grandparents, let alone of Avraham, modern American Jews facing self-induced extinction, blissfully whistle past the graveyard and espouse causes and struggles that can only further dim the Jewish spark still remaining within us. We were meant to represent godliness, morality, goodness, tradition, loyalty, and family in the world. These were the prime beliefs of Avraham and through his behavior, the rest of humanity came to recognize and even adopt these values.