Let us first discuss briefly the science behind the project. The Y-chromosome looks like a fuzzy lowercase “y” with small strands of DNA material looking like hairs sticking out from the arms of the “y”. Only males have Y-chromosomes, thus, unlike the remaining chromosomes which are mixed in each generation, each male inherits his “y” only from his father. Each “hair” of DNA on the Y-chromosome always occurs at the same place so that locations (called short tandem repeat or STR markers) can be numbered just like street signs. When you see the extensive charts of numbers such as 13-24-14-10 that means that at the first listed location the STR was 13 units long of repeating DNA; the second location was 24 units long, etc. There is no magic order in which STR data is presented; we use the Family Tree DNA (www.familytreedna.com) order convention for the first 68 numbers (markers) because Family Tree DNA has been our primary lab for STR testing since 2003.
The significance of the numbers is very simple: the larger the fraction of them that match between two people, the more closely the two people are related.
As the genetic structure of the Y-chromosome is being replicated, slippages or mutations occur. By definition mutations are random and can happen once each generation or once in a thousand generations. Thus, all of our answers are based on probabilities rather than fixed mechanical calculations.
Persons are also identified by "Haplogroups" like R1a or I:M223. The last common ancestor of people in different haplogroups lived tens of thousands of years ago.
The mutations on the Y-chromosome do not identify us as blonde, brunette, redhead, tall, short, thin, stocky, swarthy or fair, smart or dull. There is no first or last prize for having the most or fewest mutations from a single common signature.
You have probably read about "genetic testing" or "genetic counseling" for various diseases. The parts of the Y chromosome tested for genealogy purposes are not related to any disease. However, one marker, DYS464, is very rarely related to male infertility. If you already have children, this of course cannot be a worry to you. In any case, the probability of this being detected is extremely small.