UFOs are simply unidentified flying objects, and so any object in the sky that we cannot identify is by definition, a UFO. They are sometimes called UAPs (Unidentified Aerial Phenomena), since the term UFO is sometimes seen by scientists as discredited. For scientists UFOs are not articles of belief or unbelief. Like all other phenomena it is a question of examining the evidence, putting forward hypotheses, and testing the facts against those hypotheses.
Typically, unidentified objects are seen as lights or objects that seem not to be planes, helicopters, balloons or any other known man-made flying object, or objects that appear to by flying in ways that are not possible according to the known laws of science.
Most UFOs are eventually identified (becoming IFOs, one assumes). They often turn out to be weather balloons catching the light in unexpected ways, planets, which appear as extremely bright lights in the sky under some climatic conditions, comets, space junk, aircraft contrails, or meteorites. Some photographs of UFOs are later proved to have been hoaxes (and faking of photographs is becoming much easier with programs such as Photoshop, which almost everyone has access to these days).
Most UFOs are eventually identified, but not all of them, and some remain unexplained even after many years of investigation. (The websites suggested below for further reading describe many of these unexplained phenomena, which remain Unidentified Flying Objects.)
There are a number of theories about what these objects might be, but most theories suggest that UFOs are intelligently controlled craft not of Earthly origin. The most common theory is that they originate from civilisations elsewhere in the galaxy. Other theories suggest UFOs are vehicles flown by beings living inside the Earth, or by beings in a parallel Universe.
The theories are difficult to test, but it must also be said that while UFOlogists accept any report without question, many scientists dismiss them without scientific investigation, and scientists who do take the phenomenon seriously risk being ridiculed. Since most UFO sightings are fleeting and often leave no physical evidence other than photographic or video evidence, this can also make investigation difficult.
Nevertheless, there have been scientific investigations, by organisations such as the CIA and bu US, UK and French air forces. One of the first serious studies was that done in the UK by the ‘Flying Saucer Working Party’