The specifics vary from program to program, but basically an artist-in-residence usually means you're given somewhere to live, some to money to live on, and a studio to work in for a set period of time. This can be anywhere from a week to a year. In return you may be expected to teach, donate a painting, hold an exhibition, or simply work in an open studio so people are exposed to an artist, so they can watch you at work and talk to you. Again, it varies.
The benefit to an artist is that it takes you out of your usual routine and away from your everyday stresses. It exposes you to a new environment and your work to new people. Sometimes there's more than one artist in residence at a time, sometimes it's just one.
Whether being an artist-in-residence is something you'll find beneficial only you can decide, based on your personal circumstances and style of working. How do you find an artist-in-residence program? There are lots around, all over the world. Start by doing a web search on the keywords "artist-in-residence", plus a location if you want to be somewhere specific.
As an example of what you could expect, read the details of the Durham Cathedral artist-in-residence program.
