What is the purpose of a 50mm lens for nikon 5100?

What is the purpose of a 50mm lens for nikon 5100?

It is the favorite lens used by portrait photographers using cropped sensor dSLR's like your D5100

Actually need at least 2 numbers to describe any lens. Focal length which you have mentioned as 50mm but what about the aperture or f number? Are you talking about about 50mm f/1.8?

As other answerer mentioned, it is mostly used for portrait photography. However it can be used in other two situations too 1) to shoot objects too in low light. 1.8, 1.4, 1.2 are fast lenses and they work very well in low light. You can use that lens without using flash or artificial light in many situations where a kit lens would miserably fail. 2) To attain better control over depth of field. Prime lenses like 50mm are normally fast lenses (which lower f number which means aperture opens wide open) and also provide you very nice background blur/bokeh. This comes very handy for portraits but can be used to shoot anywhere you need very shallow depth of field.

Here is a photo that shows how the rose stands out in the photo. Such isolation/limited depth of field can be attained only with wide open aperture that prime lenses like 50mm, 35mm offer.

Fixed length lenses, along with the answers you already have, add ease of use to the experience. You spend more time composing the shot when you have one less variable to care about. It also makes camera easy to maneuver, carry around and putting it into a DSLR bag as well.
Just trying to add the 2 cents I did not see come from somewhere else.

Usually close-up portraits but you can use for anything if you know exactly what you are doing.

The same as any other lens… To focus the light onto the image sensor inside your camera.