Gambit

A gambit (from ancient Italian "gambetto", meaning "to trip") is a chess opening in which a player sacrifices with the aim of achieving a subsequent advantage. The word "gambit" is also sometimes used to describe similar tactics used by politicians or business people in a struggle with rivals in their respective fields, for example "The early election was a risky gambit by Theresa May".
Terminology.
The word "gambit" was originally applied to chess openings in 1561 by Spanish priest Ruy López de Segura, from an Italian expression "dare il gambetto" (to put a leg forward in order to trip someone). López studied this maneuver, and so the Italian word gained the Spanish form "gambito" that led to French "gambit", which has influenced the English spelling of the word. The broader sense of "opening move meant to gain advantage" was first recorded in English in 1855.
Gambits are most commonly played by White. Some well-known examples of a gambit are the King's Gambit (1.e4 e5 2.f4) and Evans Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4). A gambit employed by Black may also be named a gambit, e.g. the Latvian Gambit (1.e4 e5 2.Nf3 f5), or Englund Gambit (1.d4 e5); but is sometimes named a "countergambit", e.g. the Albin Countergambit (1.d4 d5 2.c4 e5) and Greco Countergambit (the original name for the Latvian Gambit). Not all opening lines involving the sacrifice of material are named as gambits, for example the main line of the Two Knights Defence (1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 Na5) in which Black sacrifices a pawn for active play is known as the "Knorre Variation", though it may be "described" as a "gambit". On the other hand, the Queen's Gambit (1.d4 d5 2.c4) is not a true gambit as Black cannot hold the pawn without incurring a disadvantage. As is often the case with chess openings, nomenclature is inconsistent.
Strategy.
Gambits are described as being "offered" to an opponent, and that offer is then said to be either "accepted" or "declined".
In modern chess, the typical response to a moderately sound gambit is to accept the material and give the material back at an advantageous time. For gambits that are less sound, the accepting player is more likely to try to hold on to their extra material. A rule of thumb often found in various primers on chess suggests that a player should get three moves (see tempo) of for a sacrificed pawn, but it is unclear how useful this general maxim is since the "free moves" part of the compensation is almost never the entirety of what the gambiteer gains. Often, a gambit can be declined with no disadvantage.
Soundness.
A gambit is said to be 'sound' if it is capable of procuring adequate concessions from the opponent. There are three general criteria in which a gambit is often said to be sound:
An example of a sound gambit is the Scotch Gambit: 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4. Here Black can force White to sacrifice a pawn speculatively with 4...Bb4+, but White gets very good compensation for one pawn after 5.c3 dxc3 6.bxc3, or for two pawns after 6.0-0 inviting 6...cxb2 7.Bxb2, due to the development advantage and attacking chances against the black king. As a result, Black is often advised not to try to hold on to the extra pawn. A more dubious gambit is the so-called Halloween Gambit: 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.Nxe5 Nxe5 5.d4. Here the investment (a knight for just one pawn) is too large for the moderate advantage of having a strong center.