One of the biggest reason to get a fast lens is the ability to capture a wonderfully blurred background or as its also called bokeh.
For this photo i used the wonderful Nikkor 105 2.5 manual focus lens at the wide open (2.5) setting and its looks great!
The thing one needs to understand about depth of field is that its a mathematical formula that is based on the focal length of the lens, the speed of the lens and the distance between your subject and your lens.
Lets use the 105mm lens as a example: it has a minimum focus range of one meter, that means that if you focus on a object that is one meter away and use the lens wide open you will get a wonderful blurred background like the picture beneath you.
The more you increase the objects distance the less bokeh you will get until you reach the infinity setting where everything is in focus.
The best way of learning this is to use the trial and error method where you take allot of photos and learn how this works because it is confusing at first.
When you are ready for digging deeper then there is a bunch of depth of field calculators online, apps for you smartphone for you to discover and play and really go deep into this subject.
If you feel brave also look at the massive wikipedia article:
iphone/ipod touch app: