Of course it can be done. It just might be cheaper to buy a ready made one though. What kind of light do you want, do you actually want to physically track a person by having the light follow them, or just have the light come on when you enter the area, because those kinds of lights are cheap.
If you want to make a basic light that detects presence you will need a passive IR sensor of the kind used in alarm systemshttp:// http://en.wikipedia.org/wiki/Passive_infrared_sensor#PIR-based_motion_detector
You will have to interface this to a relay.
For a more complex tracking system you will need some kind of servo mechanism to pan and tilt the light and allow it to follow the person, using stepper motors perhaps.
Detecting the person will be the hard part though. You could use a couple of PIRs and then look for the hot spot by devising an algorithm that takes several measurement, but this can easily be fooled by a false heat source.
The ideal way would be to use a video camera and get some pattern recognition algorithm to trac the person. Again a bit complicated. Or you could get the person to wear a marker and track that using again using a PC much like what they did on an episode of Prototype This http://videos.howstuffworks.com/discovery/33985-prototype-this-optical-glyph-tracking-video.htm
Then you could feed this data to an Arduino via the Serial interface and use that to control the servos with an algorithm that you will have to develop that will actually follow the target.
Thats one solution there are surely others.
Actually sounds like a cool project the more I think about it.