Why we have the periodic table:
In the early nineteenth century, John Dalton would add his own two cents worth to a debate that had continued since the time of Aristotle and Democritus. The question being: What is all the matter of the world composed of? Dalton would side with Democritus in the dispute, suggesting that all matter was constituted of infinitesimally small particles which Democritus had called "atomos," and which we today refer to as "atoms."
Studying the composition and properties of gases, solids and liquids, Dalton identified the specific atomic weights of hydrogen, oxygen, nitrogen, carbon, sulfur, and phosphorus. All of a sudden, the then new science of chemistry was expanding with logarithmic progression, and the search to identify all of the different elements was on. But what were the relationships between all of these atoms of elements, and why did they act differently with varying conditions. There was much yet to learn.
Fortunately, the Serbian born chemist Dmitri Mendeleev came on the scene in 1834, and would become the guy to put everything in perspective. By this time, quite a few if not most of the elements had been isolated and identified and their atomic weights established, but it would take Mendeleev's diligent efforts to understand the behavior of these atoms in an effort to ascertain their properties. In the process, he developed an organizational chart of elements which showed their relative position according to Dalton's atomic weight, but also by association of properties. Mendeleev's organizational chart even predicted the existence of some yet to be discovered elements. Mendeleev's chart would become very useful to chemists, and a modified form of it called the "Periodic Table" is still used today.
The periodic table, in contemporary terms, could be viewed as the holy grail in the science of chemistry. It is the first thing that students of the discipline will be introduced to, a facet that their instructor will require them to memorialize, and a tool which they will rely upon. It is representative of the universal language of chemistry and can likely be found hanging at the front of chemistry classrooms round the world. It is a document that provides a wealth of knowledge about the basic constituents of matter, and how they will react with each other to form compounds. Each square on the chart lists a single element, its' symbol, atomic weight, (amu) or dalton (Da) as is used today, and its electron configuration. The elemental squares are then arranged in rows and columns respective of the elements' atomic number, physical properties (metal, non-metal, or inert gas), and electrical properties based on the ordering of electrons within orbital shells. This last attribute also defines the electrovalence of the element, which establish its propensity for reactivity and interactive protocol in the formation of forming Ionic and covalent bonds with other elements.
And so in summation, I guess the best answer to the question: "Why we have a periodic table," is that this document represents in aggregate, the Rosetta stone of Chemistry. If you want to understand the complexity of the elements which make up the known universe, the Periodic Table will be your starting point, and a trusted reference thereafter.
REFERENCES AND FURTHER READING:
Pete Moore, "E=mc2 -The Great ideas that shaped our world," Friedman/Fairfax, New York, 2002