A number indicating the brightness of a star or extended object. The larger the positive number, the fainter the star or object; while the larger the negative number, the brighter the star or object. A one digit magnitude change indicates a 256% difference in brightness. 4th magnitude stars are often the faintest visible to the naked eye from a light-polluted suburb. 14th magnitude stars, by comparison, are a mere 1/10,000th as bright! 6th magnitude stars are typically the faintest naked eye stars visible from a reasonably dark sky observing site. The Sun has an apparent magnitude of -26.5.
On extended objects (galaxies and nebulas), the magnitude is the one the object would have if all its light was gathered into a single point, like a star. A 9th magnitude galaxy, therefore, will appear dimmer than a 9th magnitude star because its light is spread over a larger area than the star. A good example is M33, the face-on spiral galaxy in Triangulum. It's a 6th magnitude object, but is often difficult to see in even an 8" telescope (whose visual limiting magnitude is 14), because its mag 6 brightness is spread over nearly one square degree of sky. Such an object is said to have low surface brightness and is quite often masked by light pollution when observing from city or suburban sites.

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