he word "organic" shares a root wiith "organism" - the field has always been related to living things. In the late 18th and early 19th century, as chemistry was being born as an independent science, carbon-containing molecules seemed somehow different from other compounds. Because there are so many possible formulas for organic molecules, the Law of Multiple Proportions was less clear. Furthermore, it was far more difficult to synthesize organic molecules and it was thought that some special "vital principle" was required. This was famously disproven in 1828 by the first synthesis of an organic molecule from non-organic components.
Organic chemistry is still the chemistry of life. Since all living creatures are made of mostly organic materials, anyone who wants to study the moleclar aspects of biology, including human biology and medicine, needs to do organic chemistry. Commercially, the most important application of organic chemistry is in the petroleum industry. Since petroleum (and coal and natural gas) is the ancient remains of living creatures, this too harkens back to the original term.
Today, the term "organic" in common usage typically means food grown without artificial fertilizers or pesticides. Some chemists chuckle at this, since most of those fertilizers and pesticides are products of organic chemistry. And we wouldn't want to eat inorganic food.
But why do all organic molecules contain carbon? Or, to put it another way, what's so special about carbon that it is that important to life?
That last point deserves additional explanation. Carbon's single bonds with itself and with other elements are quite strong, but not so strong that any one compound dominates. Let's compare carbon to its periodic table cousins silicon and nitrogen.
Si-H and Si-Si bonds are reasonably strong, but the Si-O bond is so strong that most of the earth's silicon is locked in silicate rocks. A favorite trope of science fiction is the possibility of life based on silicon chemistry instead of carbon chemistry. Unfortunately for silicon-based space aliens, its reaction with oxygen is so much more exothermic that the poor creatures would burn like match heads in Earth's atmosphere.
The N≡N triple bond, on the other hand, is so stable that most nitrogen is tied up in the elemental form. Compounds with many N-N bonds are scarce and highly reactive, readily breaking down to nitrogen gas.
Because carbon atoms can form long and branched chains, there are billions of possible molecules that could be constructed from just a few C and H atoms. A helpful way to think about organic molecules is to consider them as a combination of carbon chains with functional groups here and there. Organic chemists have figured out that there are common patterns of reactivity and physical properties that happen whenever an organic molecule has a particular group of atoms. For example, the group -CO2H always acts as a weak acid, making compounds containing it acidic. The most familiar example is acetic acid , a 5% solution of which is vinegar. Most carboxylic acids have, if they are volatile, a sharp, sour, or unpleasant odor. Acetic acid shares the same group as butyric acid , the molecule responsible for the sharp smell of swiss cheese (in small quantities) or vomit (in larger concentrations).
As those examples indicate, carboxylic acids have a strong taste. Other examples of carboxylic acids are citric acid (lemons, oranges) and malic acid (sour candy). In fact, the German word for acid is "sauer" as in sauerkraut, made sour by the lactic acid that forms as it ages.
Much of what you'll study in organic chemistry has to do with the reactions of the functional groups, and their influence on the properties of molecules. In fact, many textboooks take a functional group approach to their organization, so that each chapter focuses on a small set of functional groups and considers their structure and bonding, influence on physical properties, ways of making them, and the reactions they can do to transform them into other functional groups.