Basically, Hong Kong was British colony returned to China in 1997. During the time as a colony, Hong Kong operated under British law. When it came time to be returned to China, HKers obviously didn't want to just become part of China. So a deal was made operate under a 'one country, two systems' method going forward. Hong Kong has a mini constitution that details the powers the rights people enjoy under Hong Kong, and the degree of interference China can have with Hong Kong. So our current system has separation of powers (administrative, judicial, and legislative branches), unlike China. Chinese national laws do not apply to us because we have our own legal system. We also have our own government (which answers to China), and no censorship on the internet etc.
Within the mini constitution, there is a provision that says things would remain relatively unchanged for 50 years (until 2047). However, a lot of Hong Kong people believe that China is starting to exert more and more power on Hong Kong, in breach of the promise made prior to the handover.
The current fiasco comes from a now-withdrawn extradition bill that would have meant China can extradite people from, despite no extradition treaty being made with them. People were afraid of China claiming people committed crimes then extraditing them to the lawless and corrupt China, so over 1 million people took the streets multiple times to protest (total population of HK around 7+ million). The dumbass leader of Hong Kong (called the Chief Executive) refused to withdraw the bill for a long *** time, and made people really pissed off, and this ended up bringing up a lot more deep rooted anger people had against the government, leading to today.
Source: me, from Hong Kong