Half double crochet (US terms) is a mid-height crochet stitch worked by yarning over before inserting the hook, then pulling through all three loops at once. It sits between single and double crochet, giving a slightly textured, warm fabric.
Half double crochet is a favorite for hats and cowls because it's a touch taller than single crochet — so it grows faster — while staying denser and warmer than double crochet. In UK terms it's called 'half treble.'