A recession is when your neighbor loses his job. A depression is when you lose yours.

Thanks to Greg Mankiw:

Recession or Depression?

A student asks,

What makes a recession officially turn into a depression?

There is no official designation of depression. The NBER business cycle dating committee, of which I was once a member, picks thebusiness cycle turning points. That is, with the benefit of hindsight, the committee says when the economy switches between expansion and contraction. Traditionally, milder contractions are called recessions and more severe contractions are called depressions, but there is no official word on which is which. Perhaps the clearest definition is this:
A recession is when your neighbor loses his job. A depression is when you lose yours.