Ursula Länsman, member of the Sámi Band Angelit, describes it very well. http://www.folkworld.de/9/e/sami.html
"A yoik is not merely a description; it attempts to capture its subject in its entirety: it's like a holographic, multi-dimensional living image, a replica, not just a flat photograph or simple visual memory. It is not about something, it is that something. It does not begin and it does not end. A yoik does not need to have words — its narrative is in its power, it can tell a life story in song. The singer can tell the story through words, melody, rhythm, expressions or gestures."
In one of the earliest published Sami texts, Johan Turi describes it as "the art of recalling other people." But in the past the Sami also joiked animals, landscapes, and weather. The earliest joiking was unaccompanied voice, but in the last twenty or thirty years it's been backed by many different instruments and performed in a variety of styles. There's even Sami rapping now.
Ande Somby is a Norwegian Sami lawyer and musician. He writes about joiking in this article on the Web. http://www.uit.no/ssweb/dok/Somby/Ande/95.htm
Although I described the general idea behind joiking in The Palace of the Snow Queen and mentioned two powerful modern singers––Mari Boine from Norway and Wimme from Finland––who've taken the traditional form to new places, my descriptions aren't the same as experiencing the sound of the joik. Here are some links to sites where you can learn more and hear samples:
Arran has a comprehensive list of Sami musicians, both traditional and contemporary, including their web sites and Myspace pages where you can listen to streaming mp3 tracks and download. http://home.earthlink.net/~arran4/siida/sami-yoik.htm
Another possibility to hear joiking on-line is at Amazon: Folk Music In Sweden, Vols. 21, 22, 23: A Presentation Of Saami Folk Music
Although this 3-volume collection of traditional acoustic joik is not available for purchase, the nearly 200 songs, on everything from reindeer to weather to love, and sung by a rich variety of male and female voices, is there for the listening. It's a great introduction to the form.
On Amazon, you can listen to samples from the albums of Mari Boine and Wimme too. Better yet, you can go to the website of NorthSide, an independent music company based in Minneapolis. Their focus is Scandinavian folk and new music, and they have an awesome deal: three collection of Nordic music from all over Scandinavia, which includes some cuts by Sami singers. Nordic Roots 1, 2, 3. each only $5. They also carry the full discography of Boine and Wimme.