Always an important and interesting element, hydrogen has gathered increased notice in the public eye with the focus on hydrogen fuel cells and hydrogen cars. Surely people long to learn more about this "magic" chemical that will simultaneously help free us from gasoline and pollution.
Hydrogen is the simplest atom, having but a single proton and a single electron. Normally it is found with no neutrons, but isotopes with one (deuterium) and two (tritium - which is radioactive) neutrons are known. Elemental hydrogen consists of two hydrogen atoms, bound together by a single covalent bond. (Hydrogen can only make one bond, since it has but the one electron.)
Hydrogen is the most versatile of all elements. Most elements are readily classified as metal, non-metal, or metalloid. (Each group has a set of general properties.) Not so with hydrogen.
Most periodic tables place hydrogen in the first group. (First element, first group - that seems to make sense.) This group - the alkali metals - does share some chemistry with hydrogen. They all have just one electron in their outermost (or valence) "shell". All will react with electronegative elements to give up that outermost electron, becoming a singly charged positive ion. Hydrogen does this regularly. The hydrogen ion that results is really just a single proton, and is often referred to as such by chemists. The chemistry of the hydrogen ion is of great interest. Most people are familiar with the pH scale - our way of measuring acidity in soils and solutions. The "H" in pH specifically refers to Hydrogen, whose chemical symbol is H. (The "p", if you wondered, is a mathematical function, corresponding to "the negative logarithm of ______", in this case, the activity/concentration of the hydrogen ion in solution.) Solutions with more hydrogen atoms are more acidic. For the record, the hydrogen atom does not exist freely in water, it is always coordinated with water molecules. Sometimes the complex that forms is referred to as the "hydronium ion".
On fewer periodic tables, hydrogen is listed in the seventh group - the halogens. Halogens are non-metals. They are each one electron away from achieving a stable outer shell of electrons. (Hydrogen reaches a full, stable shell once it reaches two electrons.) In the elemental form, each exists as a diatomic molecule, as hydrogen does. Halogens will react with metals to "steal" an electron, acquiring a net charge of negative one. When hydrogen forms an ion in this way, it is referred to as the hydride ion, to distinguish it from the positive hydrogen ion. Also like the halogens, hydrogen forms covalent bonds with carbon. (Unlike the halogens, these bonds are almost completely unpolarized.) This is terribly important to us, as this is not only the foundation of organic chemistry, but also the backbone of life. (That's right, you're built out of carbon and hydrogen, as well as oxygen and others that aren't at all relevant right now.)
Hydrogen reacts with oxygen, of course, to make water. This is the driving reaction behind fuel cell and hydrogen vehicle technology. Both gasses, the two explode when combined and given an ignition source. That explosion is harnessed to drive a motor or generator. In reverse, water can be broken down to re-release the gas by passing an electric current through it. Since water is abundant on Earth, we have a vast supply of hydrogen at our disposal, but the process of making the hydrogen actually uses more energy than is gained by burning it, it is not efficient over all. (This can be countered if the power used to break down the water is from a source like solar or wind.)
Hydrogen exists as a gas except under extreme conditions. Under pressure, at temperatures near absolute zero (20 K, where 273 K is "zero" Celsius or 32 Fahrenheit) it can be forced into the liquid state. This is better for storage and transport purposes than the gas, as it takes up much less space than the gas.
Hydrogen is plentiful not only on Earth, but throughout the universe. In the vast emptiness of space, hydrogen is present in a very low concentration throughout. More spectacularly, and unlike "American Idol", hydrogen is the stuff stars are made of. Hydrogen is the primary fuel for fusion in stars, leading to the formation of helium (the element, not the website). If fusion reactors ever become a reality on Earth, it truly can be "clean" energy. (Fusion bombs, it should be noted, are not clean, because they still require a uranium/plutonium fission trigger.)
Hydrogen is not only important as a chemical, but it has also served as the model upon which we have built much of our modern understanding of atoms. When we predict probabilities for electron orbitals, we do so based on the application of rigorous math to the hydrogen atom. More complex atoms make the math exponentially more difficult, so basic modeling relies on hydrogen and extrapolations.
Historically, hydrogen also ushered in the era of lighter-than-air travel. Being the lightest element, balloons of hydrogen float even better than helium balloons. Zeppelins were invented and successfully used for travel - until the spectacular explosion of the Hindenburg tragically highlighted the danger of traveling around beneath a vast quantity of highly flammable material. (The modern blimp is a helium-based descendant of the zeppelin.)
All told, hydrogen impacts our lives in a variety of ways. Aside from being crucial to life, it has driven science and technology in the past, and appears likely to do so well into the future as well.