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Definition
Long period comets are those that appear only once within reach of the Earth's orbit, or at least only once within a reasonable period that humans are likely to remember. Their orbits around the Sun take from hundreds of years to hundreds of thousands of years to complete. Despite the large periodicity of their orbits, they still remain gravitationally bound to the Sun.
Origins
Long period comets originate in the Oorts Cloud, which begins in the far reaches of the solar system and continues up to 100,000 astronomical units farther out into the galaxy. The cloud formed during the early years of the solar system and is made up of the icy and rocky planetesimals which were deflected from the inner solar system by the gravity of the giant planets, such as Jupiter and Saturn.
Orbital Shape
Long period comets have a high eccentricity, passing close to the Sun during their perihelion, which is the stage when the comet passes closest to the Sun. They are very far from the Sun during their aphelion, the part of their orbit when they are most distant from the Sun. Long period comets' orbits have a shape similar to a parabola, an infinitely long ellipse. Their orbits assume this shape because they have been stretched by the gravitational pull of nearby stars.
Example
Hale-Bopp is an example of a long period comet that recently passed within the vicinity of the Earth. In 1997, the comet came within 122 million miles of the Earth, and was observed to have a large nucleus -- estimated at 18 to 25 miles across -- and produced a large amount of dust and gas. The orbital period of Hale-Bopp has been calculated to be as long as 3,600 years.