A pip (short for "percentage in point") is the smallest whole unit of price movement in a forex pair. For most currency pairs, one pip is a change of 0.0001 — so if EUR/USD moves from 1.0850 to 1.0851, that is one pip. For pairs that include the Japanese yen, one pip is 0.01 instead, because yen prices are quoted with only two decimal places.
Pips are how traders measure profit and loss: if you buy EUR/USD at 1.0850 and sell at 1.0900, you have made 50 pips. The actual dollar value of those 50 pips depends on your lot size — a standard lot (100,000 units) gives you about $10 per pip on most USD-quoted pairs, a mini lot is $1, and a micro lot is $0.10.
Modern brokers also quote in "pipettes" or fractional pips — a fifth decimal place for majors and a third for yen pairs. So a spread quoted as 0.8 pips is really 0.00008 on EUR/USD.