As they near the Sun and become "active" they have several apparent aspects.....
Comets are invisible to us except when they are near the Sun and most Comets have highly eccentric orbits which take them far beyond the orbit of Pluto where they seem to "disappear" for a millennia. Only short- and intermediate- period comets like Halley's stay within the orbit of Pluto for a significant enough portion of their orbits.
Meteor showers sometimes occur when the Earth passes thru the orbit of a Comet such as "Perseid" meteor shower every year between Aug. 9 - 13 when the Earth passes thru the orbit of the "Swift-Tuttle" Comet, or the "Orionid" meteor shower in October as we pass thru the orbit of Halley's Comet.
The second point of origin for comets is believed to be the KUIPER BELT. It is much closer and lies within the solar system and is thought to be very similar to the asteroid belt between Mars and Jupiter, only further out. In the 1980's several comets and asteriod type objects have been discovered orbiting the Sun at a distance of 50 to 100 times the Earth's distance to the Sun, which is outside the orbit of Pluto. Scientists now believe that most short-period comets that orbit the Sun in periods of 500 years or less could be from this area.
However, it is now known that not all short-period comets come from this area. Incoming comets can interact with planets in the solar system, which changes their orbits.
If a comet orginates in the Oort Cloud they ususally have a "parabolic orbit" (that is they follow the path typical of an object that will only visit the solar system once.) But, if large planets like Jupiter gravitationally interact with them, their orbits can be changed and they can become "caputured" by the Sun into an "elliptical orbit", returning every couple of decades or centuries to the inner solar system. Occasionally, a comet that passes too close to one of these large planets can be ripped appart, or as with the SHOEMAKER-LEVY 9 Comet/s smash into the planet itself!
All Comets have a beautiful double tail of blue (electrically charged particles) and white (dust particles).