A meteoroid is a small rocky object in space in the solar system, smaller than an asteroid. A threshold (diameter or perhaps mass) is sometimes used to distinguish the two, but the traditional difference is a meteoroid is a space object like those that produce streaks of light passing through Earth atmosphere (the streak of light is termed a meteor and the term is also perhaps used for the object itself during that brief period) and an asteroid is an astronomical body observed by telescope. I've seen threshold-diameters listed as 1, 4, 10, and 100 meters, undoubtedly influenced by whatever issue is being considered. The lower end of meteoroid sizes extends to microscopic (i.e., a micrometeoroid).
A meteorite is the remnant of a meteoroid that has impacted Earth. The distinction between the three terms is sometimes ignored e.g., the term meteor can be found referring to any of the three. And when, for an example, a micrometeoroid imbeds itself in an artificial body in space, I don't know what the proper term is. A micrometeorite is a microscopic meteorite.
A meteor shower is a bunch of meteors occurring over a short time from the same direction: meteor showers are predictable as they occur when the Earth passes through a region of the solar system where a belt of meteoroids orbit (a meteor stream), often along the orbital path of a comet, and generally presumed to be debris from the comet's activity or from a broken asteroid. This produces showers that return at the same time each year, appearing to come from the same point in the celestial sphere, a point known as the shower's radiant or apparent radiant.
Another term for meteor is shooting star, and for bright ones, fireball or bolide, these latter being those brighter than (typical) Venus, or by some criteria, as bright as the Moon, which sometimes explode in the atmosphere.