Attenuation is the degree to which yeast ferments the sugar in a wort or must. If you have 50% attenuation it means that 50% of the sugars have been converted into alcohol and CO2 by yeast. If you have 100% attenuation, all of the sugars have been consumed by yeast. Beer fermented with normal brewers yeast will never have 100% attenuation. This is important because it can help predict the final gravity and alcohol content of a beer. A yeast with low attenuation will leave a beer with more sugar and more body than a yeast with high attenuation. This can also be very helpful when selecting a yeast strain for a recipe.
Example: your beer has an OG of 1.050 and the expected attenuation of your yeast is 75%. The yeast will ferment 75% of the gravity sample (75% of 50 gravity points is roughly 38 gravity points) so your final gravity should be around 1.012 (50 -38 = 12).