Greetings Gary:
"How are these figures derived and what do they mean?"
It's based on the fact that DNA is double-stranded, as Glenn suggested. Each strand is accompanied by its compliment strand, a strand whose nucleotide sequence usually matches that of the normal strand perfectly (barring mutations).
The strands are bound together, not by permanent covalent bonds, but by special non-covalent bonds called hydrogen bonds. Because these are not physical, permanent bonds, they can be broken rather easily. In the case of double-stranded DNA, all you need is heat. The stronger the interaction between the strands, the more heat you need. Normal-compliment strands whose sequences match perfectly require the most heat. Normal-compliment strands whose sequences do not match perfectly require less heat. By combining a normal strand of one animal with the compliment strand of another animal, then determining at which temperature the strands separate, one can estimate the degree of homology between the strands.
Humans and chimps share 98% homology because a human-chimp double-stranded DNA separates, or "melts", at 98% of the temperature of a human-human DNA. The process is relative at best, and somewhat subjective, but phylogenetic trees built using melting temperatures very closely match trees created by morphological features.
Nowadays we can sequence proteins and genes themselves. In those cases where it has been possible to check melting temperature trees using protein sequences, the former have been verified by the latter ever time. The most that happens is that a few species are discovered to be convergent rather than phylogenetic, but protein sequences have for the most part verified trees constructed from melting temperatures. Therefore it is still a good general method despite its problems.
Kevin L. O'Brien