There are three kinds of pedal system:
Plain platform pedals (like yours)
Platforms + toe clips and straps
Clip-in systems (called clipless)
Racing and high performance cyclists all use clipless systems now. The MTB ones are double sided and are more practical for general purpose riding. You need special shoes with a stiff sole and a metal cleat bolted to the sole. MTB shoes have a partially recessed cleat, road shoes have the cleat protruding so walking is impossible.
For riders who do lower distances and ride at a more leisurely pace then the adantages of clipless are less apparent.
The pros are higher efficiency. The cons are that you have to use the special shoes and that beginers usually fall over when their brain gets overloaded and they forget to unclip.
I find that the intermediate solution (platforms + toe clips) works for me. It is quite efficient but I can ue any type of shoe.