Unemployment rate: number of people who are not working and are looking for paid employment.
Recession: a period of economic decline. Not as severe as a depression
Depression: a sustained period of economic decline. The economy may stop dropping but it doesn't return to normal levels of growth like a recession will.
Shares/Stocks: a part of a company. Shareholders have a say in how a company is run and earn money if the company does well.
Stock market: where stocks are bought and sold, usually handled by stockbrokers