The comets that pass close to the Sun originally came from one of two places: either the Oort Cloud or the Kuiper Belt. You can think of the Oort Cloud as a giant spherical shell surrounding the Sun that's filled with about 1 million million comets (a 1 followed by 12 zeros). Its inner and outer boundaries are not very well-defined, but the cloud's extent is roughly from about 900 thousand million miles (a 9 followed by 11 zeros) from the Sun to about 9 million million miles (a 9 followed by 12 zeros) from the Sun. The outer boundary is almost halfway to the nearest star and, for all practical purposes, is the outside edge of our Solar System. Because they are so far from the Sun, the comets in the Oort Cloud take over 1 million years to make a single revolution around the Sun. Occasionally one of these comets feels a tug by another star in our galaxy and gets pushed closer to the Sun. Since such comets are probably making their first such trip near the Sun, they are called "new" comets. Approximately a dozen "new" comets are discovered every year.
The Kuiper Belt refers to a roughly disk-shaped region that extends from just beyond Pluto's orbit out to about twice Pluto's orbit. (Pluto is about 40 times farther from the Sun than we are.) Astronomers believe that most of the comets that go around the Sun in less than about 200 years originally came from the Kuiper Belt. These so-called "periodic", or "old", comets slowly drifted closer to the Sun over time. When they start getting close to Jupiter, their paths are disturbed in a very chaotic way.
It is often not very easy to tell whether a comet originally came from the Oort Cloud or the Kuiper Belt. For example, Halley's comet has a period of only 76 years, but many astronomers believe that Halley was once in the Oort Cloud. Similarly, we think that Comet Hyakutake was probably once a resident of the Oort Cloud. But this year is probably NOT Hyakutake's first trip near the Sun because the comet currently makes a complete trip around the Sun every 20 thousand years or so, which is a fairly brief time by astronomical standards. Thus, Hyakutake does not qualify as a "new" comet.
At the center of a comet is the NUCLEUS, which is typically only about
1 to 10 miles across. Except when various spacecraft flew near the
nucleus of Comet Halley in 1986, no one has ever seen a comet nucleus
directly.
As the nucleus moves closer and closer to the Sun, it gets warmer
and warmer, which causes its ices to evaporate. When the ices evaporate,
they drag DUST particles off of the surface of the comet. Sunlight
reflecting off of these dust particles produces a COMA, which is
primarily what you see when you look at a comet.
The dust particles leaving the nucleus are pushed by light from the Sun
into a DUST TAIL. The gas molecules (like water, carbon monoxide, and
carbon dioxide) that evaporated from the ices are ionized by sunlight
(the sunlight tears off one of their electrons) and are pushed by the
solar wind into an ION TAIL.