A Mixed Economy is an economy with both a public sector and a private sector, also an economy where the state regulates the private sector, for example to deter Environmental pollution or to discourage use of Tobacco products. Mixed economies also have state intervention to try and prevent Monopoly. Most Countries in the World run mixed economies. 
The size of the private sector and the public sector vary greatly between different mixed economies. The public sector is smaller in the United States of America than it is in Scandinavian nations. Liberals and even more Social democrats favour a large public sector providing goods like Universal Health Care, high quality Education and a generous safety net to protect citizens who fall on hard times. Conservatives favour a much smaller public sector.