A genius is someone who is both extraordinarily intelligent and extremely creative. Plenty of people are smart and even intelligent, but they aren't quite geniuses because they lack the creative abilities required. Other people are creative to some extent, but they do not have the intellectual capability to harness their creativity. Some famous examples include Mozart, Isaac Newton, and Albert Einstein, who is often used as the classic illustration for this term.
The exact definition of this word is actually rather difficult to pin down, because there are no clear, subjective measures that can be used to classify who is a genius and who is not. Generally, it is assumed that one has a unique and novel way of approaching situations and the world, retooling ideas and potentially creating something so monumental that it changes the way other people think. Einstein, for example, came up with a mathematical formula that changed the face of physics.
Some people measure genius on the basis of someone's Intelligence Quotient (IQ). This measurement is far from ideal, however; many people think that IQ tests are limited, and the true test of a genius is what he or she produces in life. These individuals are also often talented in multiple fields, in which case they could also be considered polymaths. Leonardo da Vinci, for example, was a polymath, skilled in the arts and sciences. Einstein, on the other hand, focused on physics specifically.
Some people feel that geniuses are crippled by their own intelligence. It is true that some have had difficulty with social interactions historically, and some of them have interesting quirks. Being a genius does not inherently mean that someone cannot function in the world, however, and plenty of these people are perfectly capable of handling the events of a day to life, often with great success. Because many think in ways which are very different, sometimes it can be a challenge to follow a conversation with such a person.
Why one person becomes a genius while someone else remains relatively ordinary is a mystery. There appear to be clear genetic links, although environment is also an important factor. Scientific studies of the brain have also suggested that such people may have slightly different brains. Incredibly gifted individuals may be talented because their minds are actually wired differently, facilitating communication between normally isolated areas of the brain or changing the way in which information is processed. The fact that many of these people are child prodigies supports this belief, as it suggests that the groundwork for genius is laid early.