Krav Maga is a Hebrew term that can be translated as "Contact Combat." It was originally known by a Hebrew acronym Kuf-Peh-Alef-Pe, which was Anglicized to Kapap (pronounced ka-POP). Krav Maga is a reality-based self-defense (RBSD) system of unarmed combat that originates from Israel. The most commonly seen system is that which has been formulated for civilian use, as opposed to municipal (police) or military, as the emphases are different with each style.
Krav Maga was created by Imi (Sde-Or) Lichtenfeld, a Jew of Slovakian descent who emigrated to pre-statehood Israel in the early 1940's. As a champion level wrestler, boxer, and overall athlete, Imi gradually designed the Krav curriculum for about 30 years before it became popularized outside of Israel. More detailed information can be found in the Krav Maga manual written by Imi Sde-Or and Eyal Yanilov (his most senior student).
Krav Maga can be found in several Western countries, particularly the United States and Israel. There is a schism in styles between the IKMF (International Krav Maga Federation, headed by Eyal Yanilov) and the Krav Maga Association of America (headed by Darren Levine, Lichtenfeld's other senior student).
Krav schools will use different training methods, depending on the focus of the instructor. Some schools use what they call "stress-testing," where a student is put into self-defense situations while various environmental factors are used to disorient them. This can include strobing lights and loud music or noises in conjunction with an encounter by an assailant. The rationale is that since a real life may be unpredictable when faced with an encounter, training someone to focus through those distractions will make them extra prepared.
More typically, Krav classes, being part of an RBSD curriculum, will present scenarios to students meant to replicate realistic situations they may find themselves in. For example, someone may try to grab your wallet or wrist from behind while you're at an ATM, or while dealing with one assailant, another may attack you from behind and put you into a headlock or bearhug. From this point, the attacked person is taught how to neutralize or escape the situation they are in, either by counterattacking their assailant, or by using an escape technique and running away.
Students are taught both principles and specific techniques for situations.
Krav Maga typicially concerns itself with close-range, surprise encounters while standing, and emphasizes techniques and methods to remain standing rather than taking a fight to the ground. However, the basic Krav curriculum does teach basic sweeps/escapes from groundfighting situations, and many schools add other fighting arts into their curriculum to enhance the Krav core. For instance, some schools will include Brazilian Jiu-Jitsu techniques to broaden a student's knowledge of how to handle an encounter that goes to the ground. The discretion of the instructor in teaching a modified Krav curriculum can be a benefit or detriment, depending on the quality of the instructor and the techniques they incorporate. This is something that can be regarded as problematic in the Krav system, as one may not know if the techniques are "krav" or "not krav."
In general, a large majority of the Krav curriculum revolves around strikes against "high-damage areas" of an opponent, such as their nose, groin, eyes, knees, or instep. A smaller, but significant portion of Krav Maga revolves around escaping holds or chokes by an assailant, followed by strikes or escape. For example, a side headlock escape in Krav includes groin strikes and a pain-compliance technique involving an assailants nose that involves them falling to the ground if they do not release the hold. There is a very small amount of groundfighting techniques, including the "upa" escape from mount.
The civilian form of Krav Maga places a near-exclusive emphasis on unarmed defense against opponents, even when the opponent is armed with a gun or knife (or even, in one darkly humorous section of the manual, against a hand grenade!). Some fault Krav for teaching a curriculum that implies that an unarmed fighter can successfully disarm and neutralize an assailant with a weapon. The Krav manual does advocate using any available object as a weapon, and demonstrates techniques where a fighter fends off two opponents (unarmed and/or armed) using a stick. However, again, the emphasis of civilian Krav Maga is unarmed defense against assailants, as most civilians are not expected to be armed or in most cases, are not expected to fight an opponent armed with a knife/stick/handgun/assault rifle/hand grenade (all of which are discussed in the Krav manual).