We might ask, why is y-DNA is so important in genealogy research? The short answer is this: a man knows for (almost) certain which ancestors he inherited his y-DNA from - his father, his father's father, and so on back through the paternal lineage. We cannot know which ancestors gave us any of our other chromosomes. ["Almost" is addressed in the next essay about pitfalls of y-DNA testing.]
Thus if 2 men find that their respective y-DNA markers are very close, they can look back through a single branch in their lineages – the paternal line - to find their common ancestor. In contrast, if they find that they share one of the other 46 chromosomes, that shared chromosome could have come from any of the thousands of ancestors in each of their respective trees.
The following analysis shows why y-DNA is traceable in the family tree.
Each of us has 46 chromosomes: 23 from our mother and 23 from our father. But which chromosomes did we get from which parent? Can we tell, just by testing our own chromosomes, which ones came from which parent?
The answer is "No" for 44 out of 46 chromosomes: there is no way to tell which parent, grandparent, or great-grandparent any specific chromosome came from. The only exception is for the so-called "sex chromosomes". This pair of chromosomes is XX in women and XY in men. A woman gets one X-chromosome from each parent, and a man gets an X-chromosome from his mother and a Y-chromosome from his father.
Therefore, even for the sex chromosomes, women cannot know which parent gave them which X chromosome.
For a man, he can be sure that his X-chromosome came from his mother and his Y-chromosome came from his father. What about the grandparents? He can be sure that his father's father is the source of his Y-chromosome, but cannot know which maternal grandparent give him his X-chromosome.
Thus y-DNA (i.e. DNA testing on the Y-chromosome) is so important in genealogy research because it is the only chromosome that you can trace back through your family tree: it is passed along the paternal line. A man knows exactly which ancestors his y-DNA came from.
No other gene has this property: any of your other genes could have come from any branch of the family tree.
When you add the fact that a son usually takes his father's name, finding a genetic match in y-DNA with another individual is quite helpful in genealogy research: you can pretty easily find your common ancestor by looking up the paternal line of your respective family trees.
Except, not always. There are a few pitfalls in using y-DNA testing in genealogy research; these are discussed in the next essay.