What is back-focusing? Is it something I need to be worried about, or can I just live with it? How can I tell if my camera/lens is sufferring from it?
Back-focusing and front-focusing is when the auto-focus consistently is slightly off in either direction.
This problem has always existed as long as auto-focus has existed, but it has come into focus (no pun intended) with digital cameras where you can enlarge the image to pixel level and really see where the focus is.
You can test this with a simple setup of a ruler and a box of matches, or any similar objects. Put the ruler on a table and place the box standing right beside it. Focus on the box and take a picture, preferrably using a long lens and the largest possible aperture (lowest f-stop value).
box -> | o <- camera | --------------- <-ruler
Now when you examine the photo you can see where the ruler is sharp. If the auto-focus is correct, the box is in focus, and the part of the ruler that is sharp is a section in front of and behind the box, centered slightly behind the front of the box. That is because the depth of focus is slightly longer behind the subject:
box -> | | --------------- <-ruler ^ ^ |__|sharp
There's a page at focustestchart.com that goes into enormous detail about this.
The quick summary: back focus is when the focus plane is further back than you were expecting it to be (so your subject is out of focus, but something behind it is sharp). This is usually operator error, but might possibly be a problem with the lens; the page linked above gives you a way to distinguish between the two.
See also the focus test chart at http://pentaxdslrs.blogspot.com/2008/06/part-1-autofocus-adjustment-for-pentax.html. It has a slightly more accurate focus target and measures the 45 degree angle for you.
Note that it's incredibly easy to do focus testing wrong. Be careful and disciplined in following the directions.
Back-focusing/front-focusing is when your auto-focus is wrong, and focuses too far or too close. This is most visible when you're shotting with fast telephoto lenses and in other situations with shallow depth of field. Most people don't like to have their photo out-of-focus, so if you're suffering from this it's best to fix it.
As Matt writes, you can check your camera+lens using chart at focustestchart.com. On some cameras front-back focusing can be tuned directly in their menu, but sometimes it's necessary to get the camera and/or lens calibrated in service center.