Why is bar mitzvah important to Jews?

At the age of thirteen, which is when the Bar Mitzva ceremony is held, the young man enters Jewish adulthood and becomes a full member of the adult congregation.
He reads a portion of the Torah, or a Haftarah from the Prophets, with the traditional trope (chant) and blessings. He will have been taught how to do this, as well as some basics about the Torah and mitzvot (Jewish observances). A celebratory meal is customary, and does not have to be in the same place or the same day.

The importance of the Bar Mitzva is that it is a major Jewish life-event and hopefully it will impress upon the young man the value and desirability of exploring and experiencing his heritage.
In this age of generation-gaps, rebelliousness and personal upheavals, many people and families could benefit from the wisdom of their ancient forebears. Today, the major Torah-texts and commentaries are available in translation; and there are outreach organizations and beginner yeshivas which serve to make the full breadth of Torah understandable to whoever is interested. In many instances it is the Bar Mitzva ceremony which sparks the beginning of a youngster's becoming a circumspect, courteous, knowledgeable and respectable peer in his Jewish community.

Because it celebrates a boy becoming a man.