Many articles describe the advantages of fast lenses - meant are lenses which have a wide maximum aperture and which let a lot of light in. The wider open the aperture blade, the smaller the f-number. Fast is somehow defined by being at least f-stop f/2.8 or even better with a lower aperture number than this f-stop. For every f-stop faster - full f-stops fastest to slower apertures are f/1.0, f/1.4, f/2.0, f/2.8, f/4.0, f/5.6 - the aperture hole has to double its size for each stop faster. Lenses are defined by their maximum aperture. An example is this: The 35 f/2.0 only allows in half the light of the 35 f/1.4 at its maximum aperture. 

Fast lenses need larger glass since it needs to accommodate for the larger maximum aperture hole of the blades. The size of the lens also depends on the focal length - longer focal lengths need larger glass, too. And now we see the two main disadvantages of fast lenses - weight and cost. Larger glass requires larger lens barrels, more difficult optical design, and more sophisticated quality control of the lens parts. Most modern consumer zoom lenses are slower lenses with maximum apertures between f/3.5 and f/5.6. They are light and less bulky - ideal for carry-on luggage and traveling. 

But fast lenses have a few unbeatable advantages speaking for themselves: normally lenses are sharpest a few stops beyond the maximum aperture. A 50 f/2.8 would be likely sharpest at f/5.6 or f/8. If we now have a 50 mm lens with a larger maximum aperture of f/1.4 for example, we suddenly reach the peak of lens sharpness already around f/2.8 to f/4.0! This means we can work under much more difficult light conditions with wider open apertures and also achieving the same sharpness! 

Faster f-stops allow the photographer to create much more creative photos by making use of the shallow depth of field (DoF) at wide maximum aperture numbers. The DoF at f/1.0 is so shallow that focusing on the right spot gets extremely difficult. Fast apertures are also very demanding for every autofocus (AF) system in cameras since it makes it harder and harder for the electronic focus system to determine the focus spot accurately enough. Microfocus adjustment of lens and camera together is highly recommended here to compensate for tiny camera body and lens variations which can otherwise easily lead to front- or backfocus issues. Unfortunately not every DSLR camera has this option included yet. Beautiful DoF examples can be created with flowers like the one on the left. The center is kept sharp, while the petals become more blurry with a wider aperture which gives the photo some sort of motion effect.

Bigger lenses let a lot more light pass through the sensor and the viewfinder itself! When I bought my first fast lenses, it amazed me how much brighter the view through my fast lens got. Manual focusing was so much easier! Sometimes the light transmission was so good that I had to underexpose my photos with up to -2/3 stops of exposure compensation. My 50 f/1.2 lens - it is the fastest lens which I own so far! - is a good example for this phenomena. Of course this effect is perfect for shooting in dim light conditions or especially in the night. The photo of the shell was taken under a dim light and manual focus with my 50 f/1.4 at f/2.2 without tripod support.

Often forgotten is another quite interesting positive effect of fast lenses - the very smooth bokeh effect. Bokeh derives from the Japanese and stands in photography for an aesthetic quality of blur. This effect is mostly caused by the lens design itself and by the shape of the lens aperture blades. Smaller apertures lead to more unwanted hard-edged bokeh, while fast lenses with wide maximum apertures give desirable smooth bokeh circles. A good example for this effect with a fast lens is one of my Christmas photos below. 

I used my 135 f/2.0 lens wide open at f/2.0 for this shot. The out of focus lights appear in circular or oval shapes with no sign of edges which gives a mix of unreal and dreaming effect.

It takes some effort as amateur to vest into a bunch of fast prime lenses. But I guarantee you that you will hold onto them because they enable you to take photos in a way you would not be able to do with slower zoom lenses.