The lens aperture is usually specified as an f-number, the ratio of focal length to effective aperture diameter. … A lower f-number denotes a greater aperture opening which allows more light to reach the film or image sensor. The photography term “one f-stop” refers to a factor of v2 (approx. 

Larger apertures allow for a shorter depth of field and generally better bokeh/blurred background. 

More light falls on the sensor at a wide aperture, which opens up your options in lower-light settings. Faster/more accurate autofocus, because more light is available to the focus system.
Better image quality. This is a little more complicated to explain but imagine you have an option between an f/2.0 lens or an f/8 lens.

 If you shoot the same scene with both sets to f/8, the f/2.4 will almost always be sharper and have less vignetting.

This is because lenses tend to get soft when they are wide open, and by stopping down partially you can improve both sharpness, as well as decrease the light fall-off that creates vignetting.

I recommend watching this video to make the learning experience more entertaining.    

Aperture & f/stop Tutorial

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