An espresso is a strong coffee drink made from roasted coffee beans.
When people say "espresso", they usually mean a shot of concentrated coffee that's served immediately. You'll often find it on menus at cafes or bars, and it's typically ordered as part of an afternoon pick-me-up or after meals in Italy, where the drink originated. If you order an espresso in the US or UK, the waiter might ask if you want it "straight up" (no milk), with a bit of sugar, or perhaps with some frothed milk on top to make a more indulgent treat like a latte or cappuccino.
A concentrated coffee beverage brewed by forcing hot water under high pressure through finely ground coffee.
