Males who share a common paternal ancestor will have virtually the same Y-chromosome DNA. We use the word "virtually" since occasionally there are small changes or "copy errors" that might occur with each descendant.

Those copy errors are called "mutations" and are generally harmless, but are useful for tracing one's direct paternal line.

For example, let's look at three first cousins who have the following haplotypes (where we show 22 out of 36 marker values),

11 14 12 13 29 24 10 13 13 14 12 15 12 12 13 12 12 12 14 25 19 30 ...
11 14 12 13 29 24 10 13 13 14 12 15 12 12 13 12 12 12 14 25 19 30 ...
11 14 12 13 29 24 10 13 13 14 12 15 12 12 13 12 12 12 14 25 19 31...

Note that the first two cousins have the same haplotype, but the third cousin has a difference of one marker value (31 instead of 30).

That difference would have been due to a mutation that occurred in his Y-DNA (or his father's), but not in the other cousins.

In general, the greater the number of mutations we find between two males, the further in the past their common paternal ancestor lived.