Short answers, pulled from the story.
A hedge is an investment position intended to offset potential losses or gains in a companion investment. It can be constructed from stocks, exchange-traded funds, insurance, forward contracts, swaps, options, futures contracts, and various over-the-counter and derivative products.
The word hedge comes from Old English hecg, meaning any fence, living or artificial. Its use as a verb meaning "dodge" or "evade" dates from the 1590s, and its financial sense of insuring oneself against loss in a bet dates from the 1670s.
Southwest Airlines used crude oil futures contracts and related derivatives to hedge its jet fuel costs. When fuel prices in the United States rose sharply after the 2003 Iraq war and Hurricane Katrina, Southwest saved a significant amount compared to rival airlines.
Forward contracts are unique to each buyer and seller, carry the risk of default or renegotiation, and typically result in actual delivery. Futures contracts are standardized in quantity and date, trade on exchanges, are guaranteed by clearing houses, and almost never result in physical delivery, allowing parties to exit the contract early.
A natural hedge reduces risk by matching cash flows rather than using a financial instrument. Examples include an exporter opening production facilities in its sales market to align revenues and costs in the same currency, or an oil producer paying employee bonuses in U.S. dollars to match the currency of its revenues.
The long/short equity pairs trade involves buying shares in one company while simultaneously short-selling an equal dollar value of shares in a related competitor. The goal is to profit from the relative performance of the two companies while reducing exposure to industry-wide events that would affect both stocks.