I came to learn the meaning of the word phylogenetics in 2006, when I started working on HIV. With a highly variable virus like HIV, it is convenient to be able to reconstruct its molecular evolution through a graph called phylogenetic tree. It gives researchers a visual sense of the genetic diversity found in the sample of viral sequences and infer what the infecting strain (the "patriarch", so to speak) might have looked like.
These trees are not specific to virology. In fact, they are used in all fields of evolutionary biology to infer genealogical and evolutionary relationships. A recent paper in PNAS  discusses the "Scientific, historical, and conceptual significance of the first tree of life." From the abstract:
"In 1977, Carl Woese and George Fox published a brief paper in PNAS  that established, for the first time, that the overall phylogenetic structure of the living world is tripartite. We describe the way in which this monumental discovery was made, its context within the historical development of evolutionary thought, and how it has impacted our understanding of the emergence of life and the characterization of the evolutionary process in its most general form."By comparing molecular sequences of different organisms, Woese and Fox constructed the very first tree of life and showed that all species are phylogenetically related. Using the tree, they divided all cellular life into three major groups: eukaryotes (organisms whose cells have a nucleus), eubacteria (non-nucleated cells, or prokaryotes), and archaebacteria (a kind of prokaryote that shares similarities with eukaryotes -- I know, it gets complicated!). Interestingly, the paper went almost unnoticed at first, and then, when it did get noticed, it was highly criticized, as often revolutionary thinking is:
"The manuscript received severe criticisms when it was submitted to PNAS in the summer of 1977. One reviewer recommended that it not be published on methodological grounds that their claim for a tripartite division of the microbial world was as unfounded as their claims in regard to symbiosis and the origin of eukaryotic organelles."It should be said that comparing genetic sequences back then wasn't as straightforward as today (hence the skepticism), and that, though not systematically proven, the general belief prior to this paper had been that life could be divided in two, not three, major groups.
Woese realized very early that the only way to quantify evolutionary change was to study the conservation and variation of molecular sequences across different organisms. So, together with Fox, they looked at small subunit ribosomal RNA from different organisms. In all cells protein synthesis is carried out in the ribosomes, which create proteins reading the information from the messenger RNA (mRNA). Ribosomes have an RNA component and a protein component, and ribosomal RNA, or rRNA, as you may have already guessed by now, is the RNA component of the ribosome.
Woese and Fox set the foundations that, years later, led to the discovery that the root of the tree of life was to be found in the eubacterial line and settled the question of whether chloroplast and mitochondria originated from a symbiotic event. Pace et al. conclude in :
"Modern versions of the techniques used by Woese and Fox are now routinely used to sample environments as varied as geothermal hot springs and gastrointestinal microbiomes, providing unprecedented insight into community structure and dynamics. The results challenged the foundations of classical evolutionary theory, requiring new modes of evolution to be considered, indicating the presence of an unexpectedly large microbial pangenome (field of genes‚ to use Woese's favorite phrase), and forcing us to reconsider basic concepts such as the nature of species. Perhaps no other paper in evolutionary biology has left a richer legacy of accomplishments and promise for the future."
 Pace, N., Sapp, J., & Goldenfeld, N. (2012). Classic Perspective: Phylogeny and beyond: Scientific, historical, and conceptual significance of the first tree of life Proceedings of the National Academy of Sciences, 109 (4), 1011-1018 DOI: 10.1073/pnas.1109716109
 Woese, C., & Fox, G. (1977). Phylogenetic structure of the prokaryotic domain: The primary kingdoms Proceedings of the National Academy of Sciences, 74 (11), 5088-5090 DOI: 10.1073/pnas.74.11.5088