Roughly 22,000 meteorites have been found on Earth, of which 15 are known to have originated on Mars. They are known as SNC (Shergotty, Nakhla, Chassigny) meteorites, after the names of the locations where three of these meteorites fell. One Martian meteorite, ALH84001, falls into none of these categories, and no other meteorites similar to Chassigny have been found. Three Nakhlite meteorites have been located, and the other 10 are all Shergottites, by far the most common category of SNC meteorite. The meteorites are of particular interest to scientists studying Mars, as they represent by far the most affordable means of getting information about the planet. Space probes are expensive.
Without growing too technical, it is easy to explain the conclusion that these meteorites are indeed Martian. First, they are differentiated. Most of the small bodies in the solar system have approximately the same composition as the sun and the original solar nebula, all mixed together. To change the composition considerably requires that the rock was heated to the point of melting and had some chemical components preferentially selected over others, or differentiated. Generally, to generate this kind of heat requires considerable internal gravity. These meteorites have compositions similar to Earthly rocks, so they must have come from a planet-sized body. Narrowing the remaining candidates to Mars would not have been possible before the Viking spacecraft visited Mars in 1976. The Viking landers took detailed measurements of the Martian atmosphere, including chemical composition and isotopic ratios. When heated, the SNC meteorites will release gas identical within measurement error to the composition of the Martian atmosphere. So we're pretty confident of their origin.
SNC meteorites are thought to originate from the impacts of comets or large meteorites into the surface of Mars, with sufficient velocity to eject particles into orbit. As impacts of sufficient size are rare, the SNC meteorites are thought to originate from just a few distinct events, explaining the dearth of categories. Their times in space vary but run into the millions of years, the times being measured by the chemical results of exposure to the solar wind. A brief discussion of each of the four meteorite types follows:
This is by far the oldest of the Martian meteorites, and the one to receive most of the media attention when NASA researchers claimed to have found evidence of Martian life in the meteorite. It is a cumulate orthopyroxenite, approximately 4.5 billion years old, or very nearly the age of the solar system. Its chemical and geologic history is extremely complex, and the question of whether the evidence of life is conclusive remains unresolved. Also interesting is the question of how this meteorite survived on the surface of Mars. No rocks on Earth are as old as 4.5 billion years, and all the rocks of that age are thought to have been destroyed by plate tectonics or major impact events. It is not certain why these processes failed to destroy ALH84001 on the surface of Mars.
Shergottites are the most numerous SNC meteorites and share enough properties that they are thought to have originated from one general location on the surface of Mars. They are of similar age and geologically recent, the youngest being dated at 150 million years old. Interestingly, the Shergottites are olivine-bearing basalts very much like some rocks found on Earth.
Nakhla, the first Nakhlite meteorite, is the second-largest of the SNC meteorites, and has an amusing story of note behind it. Nakhla fell in Egypt on June 28, 1911. Through the roof of a woman's house. It killed her dog. Chemically speaking, it and the other Nakhlite meteorites are olivine-bearing clinopyroxenites, somewhat similar to the rocks that make up Earth's mantle. Nakhla is another ancient rock, approximately 1.3 billion years old, and there have been some claims of evidence for Martian life in this meteorite as well.
Well, Chassigny is another one-of-a-kind, but unlike ALH84001, isn't unfairly slighted and sneaks a letter into the SNC designation. Chassigny fell over France on October 3, 1815. Dated at 1.36 billion years old, it is an olivine-rich rock known as a dunite. Dunites on Earth are incidentally quite pretty and represent chemically depleted portions of the mantle.