Fats have the ability to "shorten" gluten strands in flour, resulting in baked goods that are tender and friable. "Short" pastries are flaky or even crumbly; good shortbread is the essence of shortness, practically melting in your mouth. So shortening is a fat that is used to render your baked goods "shorter".
While mneek is correct that shortening includes any fat that is solid at room temperature - lard or butter, for example - most products sold today under the label shortening are white tasteless affairs which are processed from animal fats or refined and hydrogenated vegetable oils, though they may contain colouring or flavouring to simulate butter. Commercial shortenings are whipped to give the product a fluffier texture and emulsified to permit better sugar absorption. Unless shortening is clearly labelled vegetable shortening, it will contain some animal fats.
If you don't have shortening when you need it, substitute another solid fat rather than a liquid fat like oil; a liquid fat will give very different results, especially with finicky recipes like pie crust.