Economists classify economies based on how resources are allocated between different uses and how the goods that result from those resources are distributed. In all economies, individuals are interdependent. How I use my resources impacts what is available for you, and everything I consume was produced by someone else using resources that I do not personally control.
The main difference lies in how people interact and how their decisions are coordinated among each other; do people answer to direct commands or plans from above or do they make their own decisions based on their own individual circumstances of time and place, as described by the economist Friedrich Hayek.1
The main three types of economies, or ways of allocating resources for society, are traditionally categorized as follows:
Planned or Command Economy
In a planned or command economy, all the resources available to the economy are allocated among different uses by some single authority (usually a government) according to a predetermined plan created by that authority. This authority could be democratically elected, though these types of economies tend to also have centralized political power. Importantly, individuals can only make decisions about how to use resources to the extent to which that is allowed for by this central plan.
Market Economy
In a market economy, there is no overarching, predetermined plan. Resources are entirely privately owned by individuals and businesses and those resources are bought and sold by those individuals and businesses in markets; those actors make their decisions purely based on their own goals and interests in response to prices determined by competition for buyers and sellers in each market. In these types of economies, each actor in the market decides what to do with their own resources, but those decisions are all coordinated with one another by prices.
Mixed Economy
Within a mixed economy, essentially all economies in the modern world include some aspects of both planned and market economies. These economies differ in the extent to which they rely on one or the other method of allocating resources. Economies exist on a spectrum, with some leaning more toward market allocations of resources and others relying more on the government to allocate resources.