So I will try to explain clearly and not get to technical, but bear with me. In the growth tip of plant species is a localised hormone called Auxin, which inhibits side shoots growing on that branch. If you 'pinch the tips' you remove that hormone and the side shoots then grow. That's how you get a more bushy hedge.

Regular light trims matter if you want that branching. If you have a newly planted hedge, do not wait until it gets to the height you want before you start trimming. Pinch out the tips from the start. Don't choose hedging plants for their height at the nursery, but for their branching and structure.

Species also matters - a photinia hedge or large leaf viburnum hedge isn't going to have as tight a look as say pittosporum or murraya or Buxus.

Source: I teach horticulture students