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Well, it unfortunately is not a simple idea to explain!
The simplest way to explain it is that it is the relative density of the water. Fresh water is less dense than saltwater, because it has less "stuff" in it. When you add salt to water, it increases the amount of salt concentration in the water, making the water more dense.
I found this article on Wikipedia, but it may do more to confuse you than answer your question...it's not extremely easy to follow.
specific gravity is also called salinity level.. You find yours with a hydrometer or refractometer. Most people keeps theres anywhere between 1.020 and 1.026. depending on what you keep in your tank may steer you on the higher end.
Top off daily with fresh ro/di water to keep the SG where you want it. You want to keep it constant that is the key here, big swings up or down can effect the tank in a negative way.