When you receive your Y-DNA results from Family Tree DNA, you will see this on your main screen. Click on “Matches” and you will see a list of men who share Y-DNA with you.
When you click on “Matches”, a screen like this comes up with a large list of men who share your Y-DNA. On the left is the “Genetic Distance”, followed by the name of the person who tested. Earliest known ancestor is based on the tester’s research on their male line. Keep in mind, our trees are based on paper and our DNA is based on genetics. It is very common to see a mixture of names here. Different names could be due to name changes many hundreds of years ago, or a non-paternal event. Why are my Y-DNA Surnames Different? 
The orange “Tip” box will give you an idea of how many generations ago you shared a common ancestor with this person. For example, a person with a genetic distance of 2 has a 100% probability that you shared a common ancestor 24 years ago and a 99% probability that ancestor was within the past 12 years. Obviously, the smaller the number, the closer the common ancestor was.
With genetic distance, I think in terms of steps on a ladder. My father tested at the 67 level. Currently, Family Tree DNA offers this test at 37, 67, 111, and 500 levels. The cost varies from $169- $649. So what do these levels mean? If your DNA were steps on a ladder and the ladder had 500 steps, you would only have them sequence the first 37, 67, 111, etc. steps. By looking at the image above, my father’s closest match is at a genetic distance of 2. If we test at a higher level, this person will still be a genetic distance of 2. If the person was a 0 genetic distance, I would be interested to see if this held true at a higher level of testing. The only motivation for me to test my father at a higher level would be to determine information I have obtained from the projects I have joined. I have touched on these “projects” in two previous posts and it is a topic requiring further discussion another time. Family Tree DNA, Why are my Y-DNA Surnames Different?
Below is an illustration to help with understanding genetic distance.
For example, if the red line indicated 67 DNA markers and the steps above go up to 111 markers, because I only tested to the 67th step, I only know how closely our 67 steps match. In this case they are exactly the same which would indicate a genetic distance of 0. However, our DNA does not match higher up. I would only know this if I tested at a higher level. Although I have a genetic distance of 0 at 67 levels, I might have a genetic distance of 2 at 111 level of testing.