The Three-Needle Bind-Off is a way to join two rows of live stitches together. It's faster and more straightforward than grafting, but it leaves a ridge that can be unwanted. When I use this bind-off in a pattern, this ridge is either essentially invisible or an intentional design element.
To work the Three-Needle Bind-Off, you'll have two pieces of knitting, both still on the needles. You'll also need a "working" needle: either a third needle in a similar size to the ones you've been knitting with or the non-working end of one of the pairs holding your live stitches.
Hold the two pieces together as instructed in the pattern, usually with the right sides together and the working yarn coming off the right edge of one of them. Line the needles holding the live stitches up parallel to one another with tips pointed toward your right and stitches near the ends, as though you were about to begin knitting.
To work the first stitch: Insert working needle into first st on each parallel needle as if to knit, wrap yarn around working needle as if to knit, knit the 2 sts together, slip first st off of each parallel needle.
With each remaining stitch: * Insert working needle into next st on each parallel needle as if to knit, wrap yarn around working needle as if to knit, knit the 2 sts together, slip first st off of each parallel needle (there will be 2 sts on working needle), use one of the parallel needles to pass first st on working needle over second and off needle (as with a standard bind-off); repeat from * until only one st remains on working needle.
Cut the yarn, thread it through the remaining stitch, and pull tight.
The following video demonstrates how to work the Three-Needle Bind-Off:
If you tend to bind off tightly or are worried about your bind-off having enough give for another reason, take a look at the three-needle version of Jeny's Surprisingly Stretchy Bind-Off, which is demonstrated in this video: