Recession is a reduction of the growth rate of GDP below that required by growth of population. They typically last 10 months and recovery takes 20 months. A Depression is technically 2 consecutive quarters of a decline in GDP. Few examples exist, but they are usually tied to banking crisis or speculative bubbles bursting.
The cliche answer is that- A recession is when your neighbor is unemployed and a depression is when you are unemployed. Since the line between the two can be blurry there is a glimmer of truth in the cliche. Economists don't all agree but difference has to do with the gross domestic product being down for a certain number of years by a certain percentage usually I think 10% for it to be a depression .