The brakes in the above photo are known as 'cantilever brakes' and were used on the majority of mountain bikes up until late 1996 when Shimano released their mass produced V-brake. Other types of brakes existed at the time too including U-brakes, roller cams and disc brakes, but V-brakes arrived in late 1996.
Prior to Shimano's first XT V-brakes there were other smaller companies who had produced similar linear pull designs before Shimano came along and made them affordable and popular.
The benefits of V-brakes are that they are easy to set up, and give more leverage at the brake itself. This means that less leverage and therefore effort is required at the brake lever. The brake levers on V-brakes have a greater distance between the pivot and cable, ie lower leverage. This is compensated by the longer arms of the V-brake which gives more leverage.
This means that with less effort from your fingers you can achieve more braking force than with cantilevers.
Without getting into the 'which is better' argument, it means that potentially for the less effort you can get the same braking power as a well set up canti. hence why they are generally seen as a design improvement.
Unfortunately cantis can be difficult to set up correctly, so many people will have, or remember having, bad experiences with them.
They can work very well but it's all about set up...