What is the point of pedal straps?
There are a number of reasons for using either toe-clips (pedal straps) or clipless pedals:


It allows you to pull up as well as down, increasing the efficiency of your pedalling. This is something that you need to work at to get full effect from, as it is not a natural motion to most people. In Cadel Evans' book "Close to Flying" there is talk of a bike he uses for training that has a "freewheel" mechanism for the cranks which forces you to practice lifting the pedals as well as pushing them.
It positions the pedal under the ball of the foot giving you better leverage. While you don't need straps or clipless to do this, it does help keep your foot in the right place.
It helps to stop your feet coming off in rough ground while mountain biking.
It gives you more control over the rear of the bike allowing you to lift and shift the rear more easily. This makes it easier to bunny hop, and helps with controlling the bike on rough ground.