What is the public and private sphere?

The basic distinction between them is that the public sphere is the realm of politics where strangers come together to engage in the free exchange of ideas, and is open to everyone, whereas the private sphere is a smaller, typically enclosed realm (like a home) that is only open to those who have permission to enter it 

How does Jurgen Habermas define the public sphere?

Habermas defined the public sphere as a virtual or imaginary community which does not necessarily exist in any identifiable space. In its ideal form, the public sphere is “made up of private people gathered together as a public and articulating the needs of society with the state”