If you pass the thread or cord through a bead only once, I call that bead stringing. You can learn more about beadstringing, and see lots of free projects on the Stringing Beads page.
What it is....
I classify "beadweaving" as anything that requires cord or thread to be passed through beads more than once.
Different knotting techniques abound, and I confess, I'm not very good at any of them :P
I don't have a lot of patience for those tiny beads and picking them up with tiny needles, but I have a lot of respect for the many patient and talented beadweavers who do.
You can find a few project links further on in this article.
What You Need to Get Started
At the very minimum, you need some strong thread, some beads, and a needle that can accomodate the thread, AND is small enough to pass through the beads a few times. This is especially tricky with seed beads, and there are specialty threads and specialty beads available that make the job of weaving and uniformity easier.
Beginners might have less frustration if they start with bigger beads. Sometimes you can skip the needle by using monfilament thread with regular beads, or thicker nylon thread with pony beads (for kids projects).
When I was a kid, everyone made bead lizards out of pony beads --simple little weaves that we'd strap onto our backpack zippers. Those bead designs took a few minutes to master, and were addicting to make. ;)
Of course, we had no idea what it was called back then. We just thought they were cool.