The specifics vary from program to program, but basically an artist-in-residence usually means you're given somewhere to live and a studio to work in for a set period of time, sometimes a stipend too (some money to live on). A residency can last 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 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. Be sure to check all the details in the "small print" before you apply.
New York artist Tracey Helgeson has several blogs about her residencies at the Vermont Studio Center. They're worth reading to share her experiences, the realities of what she managed to do compared to what she'd thought or planned, and why it can be serious creative boost.

