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A measure of how strongly an object's orbit is tilted relative to an ideal reference plane. When describing objects orbiting the Sun, that reference plane is usually the Ecliptic, while for objects such as moons orbiting planets, the plane refers to the equator of the planet concerned. Inclination is represented as an angle, where 0° describes a theoretical orbit that remains exactly within the reference plane.
Within the Solar System, the planets emerged out of the same original protoplanetary disc, and so maintained a relatively similar orbital plane to one another. This means that the major planets of the Solar System have generally low inclinations, ranging from 0.77° (Uranus) to 7.01° (Mercury). Earth is a special case, because the plane of the Ecliptic is defined relative to its orbit, so its inclination on this system is by definition zero. (Measured against the plane of the Sun's equator instead, that value rises to 7.16°.) These relatively low inclinations explain why the planets follow a predictable path through the sky, remaining within the band of the zodiacal constellations as seen from Earth.
Higher inclination values indicate more extreme departures from the reference plane, with an inclination of 90° representing an object in a polar orbit (that is, its orbital path is perpendicular to the equator, and carries it over the poles of its primary). Inclinations of more than 90° are possible, but these represent retrograde orbits: that is, orbits in which an object follows a path in the opposite direction to the rotation of the primary (inclinations like this are often given using negative angles).
As an example, the inner moons of the planet Jupiter formed alongside the planet itself, and generally show low inclinations and prograde orbits (they orbit Jupiter, that is, in the same direction that the planet turns). Of the four main Galilean moons, all of them have inclinations of less than a degree, so they remain within a tight orbital plane around the giant planet. Many of Jupiter's small outer moons, however, did not form at the same time as the planet, and represent objects later captured by Jupiter's gravity. These captured moons follow much more varied orbital paths, very often orbiting in a retrograde direction, with inclinations as much as 50° or more (in extreme cases like that of the moon Carpo) from Jupiter's equatorial plane.
Calculating an Ecliptic or equatorial reference plane is relatively straightforward for objects within the Solar System, but is less workable for more distant objects. Considering the orbits of binary or multiple stars, for example, or extrasolar planets, it can be difficult or impossible to determine the equatorial planes of the objects concerned. In cases like this a different approach is used, defining inclinations relative to an imaginary plane perpendicular to the line of sight from Earth.
By this model, and object with 0° inclination orbits its primary 'face-on' as seen from Earth, while higher inclinations refer to more narrow apparent orbital paths. A value of 90° inclination describes an orbit seen 'side on', so that an object crosses directly in front of or behind its primary (again, specifically as seen from Earth).
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