I use half double crochets a lot in my designs as they make an excellent transition from single crochet (sc) to double crochet (dc) without an apparent jump in size. They also make an extra thick sc in designs that need the bulk.
The half double crochet (hdc) is a cross between a sc and a dc. It has two wraps like the dc.
The hook is then put through the next stitch; the thread is caught from behind the working fabric and pulled through, resulting in 3 loops on the hook. Then the working thread is pulled through all three loops on the hook.