It's called sport when people exercise. It's fun, it's healthy or they compete against others. So it's not about simply getting from one place to another.
The word comes from English. It became widespread around 1900, when people used to talk about games or gymnastics. When people used the word sport, they mainly thought of people measuring their strength. It was also "sporting" if people behaved decently and nobly, even towards their opponents.
Today there are countless sports clubs. In Germany alone, six million people are members of such clubs. There they play football or handball, they swim, jump, run or throw or do one of the many other sports. The most important sports are united in the Olympic Movement. Their best athletes take part in the Olympic or Paralympic Games every four years.
Popular sport is sport that many people do for fun or for their health. Competitive sport, on the other hand, is all about winning in a competition. Very good athletes in a popular sport even practise it as a profession.