The half-double crochet stitch involves, well, half the number of times you pull your yarn through your loops the way you would if you were making a double crochet stitch. I can never quite shake the feeling that I'm doing something a little incorrectly when I have three loops on my crochet hook and then I yarnover and pull the yarn through all of them at once. But I'm not doing anything wrong because that's the completely correct way to do things when your pattern calls for the half double crochet stitch. Here, this nice lady will show you:
And that's how it's done!
See these little swatches?
This is what 5 rows of double crochet, 5 rows of halfdouble crochet, and 5 rows of single crochet look like! A double crochet stitch is twice the height of a single crochet stitch, and the half double crochet stitch (abbreviated to 'hdc' in patterns) is somewhere in between them. Not too big, and not too little. It's juuuuust right.
The half double crochet stitch is used in crochet patterns. I realize that's a pretty banal statement, but the half double crochet isn't especially tricky or mysterious or weird. If there are crocheted items to be made, there will be patterns for those items and a whole heckuva lot of them will call for half double crochet stitches. It's not quite as common as a single crochet stitch or a double crochet stitch, but it is one of the most common crochet stitches. It's a good one to know.
And now you do! Watch the video a few times and try it out for yourself. You're well on your way to being a crocheter. Happy hooking!