This post can be read in full here: http://www.ianhopkinson.org.uk/2010/07/the-periodic-table/
Understanding the Periodic Table is very much like making love to a beautiful woman, there's no point rote-learning the location of the different elements if you don't know what they do... langtry_girl*The Periodic Table of the Elements is a presentation of the known elements which provides information on the relationships between those elements in terms of their chemical and physical properties. An element is a type of atom: iron, helium, sulphur, aluminium are all examples of elements. Elements cannot be broken down chemically into other elements, but elements can change. An atom is comprised of electrons, protons and neutrons.
This is all very nice, but if you look around you: at the wallpaper, the computer screen, the table - very little of what you see is made from pure elements. They're made from molecules (pure elements joined together), and the molecules are arranged in different ways which may be completely invisible. So in a sense the periodic table represents the bottom of the tree of knowledge for people interested in materials, other scientists may be more interested in what makes up the elements.
At various times in my life I've been able to name and correctly locate all the elements in the periodic table, normally takes a bit of effort and some mnemonics to help. Increasingly now, I can remember the mnemonics but not the elements they refer to.
Different parts of the periodic table are important to different sorts of scientists. To organic chemists carbon (C), hydrogen (H), oxygen (O), nitrogen (N) hold the majority of their interest with walk on parts for some of the transition metals (the pink ones in a block in the middle) which act as catalysts. Inorganic chemists are more wide ranging, only really forbidden from the Noble Gases (helium (He), neon(Ne), argon (Ar), krypton (Kr), xenon (Xe)) which refuse to react with anything. Semi-conductor physicists are after the odd "semi-metals": silicon (Si), indium (In), gallium (Ga), germanium (Ge), arsenic (As). For magnets there's iron (Fe), cobalt (Co), nickel (Ni) along with other transition metals and the Lanthanides. The actinides are for nuclear physicists, radiation scientists and atomic bomb makers. Hydrogen is for cosmologists. In this view, as a soft condensed matter physicist, I am closest to the organic chemists.
I'm rather fond the periodic table, it is the scientist's badge, but I'm scared of fluorine.
*To be fair to langtry_girl, I pondered on twitter "Trying to finish the sentence: "Understanding the Periodic Table is very much like making love to a beautiful woman..." and I think hers was the best reply. It is, of course, a reference to Swiss Toni.