A long-period comet is a comet (Sun-orbiting object with a coma and possibly a tail) with an orbital period of 200 years or more. The longest show near-parabolic orbits, i.e., traveling at close to escape velocity, have periods determined to be many thousands of years, and orbits that are often modified during each pass through the inner solar system due to gravitational interactions with the planets. Also, unlike most solar system bodies, their orbits are often far from the ecliptic plane.
This is as opposed to short-period comets which include Comet Halley with its 76-year orbital period.
The Oort Cloud is the name given to the collection of long-period comets at the distant region where they reside for most of their existence.