Height of the eye or an object above sea level. Used to calculate distance to the horizon or an object.
Error caused by moving horizontally relative to some centerline. For example, pretend you're on deck, looking past a buoy at something on shore. Now step a few feet to the side. The buoy and the object on shore will no longer line up. That's horizontal parallax. The amount of error depends on how far you stepped and how far away the objects you were sighting are.
So how does this apply to celestial navigation? Suppose the object you're looking at is the Moon, the Sun, or a planet. And instead of stepping a few feet to the side, you moved 4000 miles (the radius of the Earth). This will change your measurements. For very far-away objects such as stars, the difference is infinitesimal. For the moon, the error can be more than a degree. The tables in the Nautical Almanac will give correction factors for the Sun, Moon and planets.
Sextant altitude, altitude of a body directly measured with a sextant. No corrections are applied.