The public sector is the part of the economy owned and controlled by the government. Business activity in the public sector varies from country to country. Often health care, postal services and the electricity network are owned and controlled by the government.
The private sector is a part of the economy owned and controlled by private individuals. Any privately owned business is in the private sector. It’s the kind of business organisation people come into contact with most day to day. McDonalds, Apple and small businesses like your local corner store, are all in the private sector.
The mixed economy describes a country with economic activity in both the public sector and private sectors. In reality, nearly all countries have a mixed economy. The variation lies in the balance between the public and private sectors in the overall economy. India has a very small public sector lower than 10% of the total economy. However, in China, estimates put government-owned activity at around 50% of the whole economy.