These people in Hong Kong are protesting because they want universal suffrage. They want to vote for their Chief Executive. They did not get it.
Universal suffrage means that every citizen above the age of 18 is allowed to vote. Most countries have universal suffrage, but some do not. In some countries people had to fight to get it. In other countries, it was granted after demonstrations in the main cities. They thought it was important to have it because they wanted to choose who ruled over them.