Strange matter is a particular form of quark matter, usually thought of as a "liquid" of up, down, and strange quarks. It is to be contrasted with nuclear matter, which is a liquid of neutrons and protons (which themselves are built out of up and down quarks), and with non-strange quark matter, which is a quark liquid containing only up and down quarks. At high enough density, strange matter is expected to be color superconducting. Strange matter is hypothesized to occur in the core of neutron stars, or, more speculatively, as isolated droplets that may vary in size from femtometers (strangelets) to kilometers (quark stars).
Two meanings of the term "strange matter" 
- The broader meaning is just quark matter that contains three flavors of quarks: up, down, and strange. In this definition, there is a critical pressure and an associated critical density, and when nuclear matter (made of protons and neutrons) is compressed beyond this density, the protons and neutrons dissociate into quarks, yielding quark matter (probably strange matter).
- The narrower meaning is that quark matter is more stable than nuclear matter. The idea that this could happen is the "strange matter hypothesis" of Bodmer  and Witten. In this definition, the critical pressure is zero: the true ground state of matter is always quark matter. The nuclei that we see in the matter around us, which are droplets of nuclear matter, are actually metastable, and given enough time (or the right external stimulus) would decay into droplets of strange matter, i.e. strangelets.
Strange matter that is only stable at high pressure 
Under the broader definition, strange matter might occur inside neutron stars, if the pressure at their core is high enough (i.e. above the critical pressure). At the sort of densities we expect in the center of a neutron star, the quark matter would probably be strange matter. It could conceivably be non-strange quark matter, if the effective mass of the strange quark were too high. Charm and heavier quarks would only occur at much higher densities.
A neutron star with a quark matter core is often  called a hybrid star. However, it is hard to know whether hybrid stars really exist in nature because physicists currently have little idea of the likely value of the critical pressure or density. It seems plausible that the transition to quark matter will already have occurred when the separation between the nucleons becomes much smaller than their size, so the critical density must be less than about 100 times nuclear saturation density. But a more precise estimate is not yet available, because the strong interaction that governs the behavior of quarks is mathematically intractable, and numerical calculations using lattice QCD are currently blocked by the fermion sign problem.
One major area of activity in neutron star physics is the attempt to find observable signatures by which we could tell, from earth based observations of neutron stars, whether they have quark matter (probably strange matter) in their core.
Strange matter that is stable at zero pressure 
If the "strange matter hypothesis" is true then nuclear matter is metastable against decaying into strange matter. The lifetime for spontaneous decay is very long, so we do not see this decay process happening around us. However, under this hypothesis there should be strange matter in the universe:
- Quark stars (often called "strange stars") consist of quark matter from their core to their surface. They would be several kilometers across, and may have a very thin crust of nuclear matter.
- Strangelets are small pieces of strange matter, perhaps as small as nuclei. They would be produced when strange stars are formed or collide, or when a nucleus decays.
See also 
- J. Madsen, "Physics and astrophysics of strange quark matter" arXiv:astro-ph/9809032, Lect. Notes Phys. 516:162-203 (1999)
- F. Weber, "Strange quark matter and compact stars", arXiv:astro-ph/0407155, Prog.Part.Nucl.Phys.54:193-288,2005.
- A. Bodmer "Collapsed Nuclei" Phys. Rev. D4, 1601 (1971)
- Edward Witten, "Cosmic Separation Of Phases" Phys. Rev. D30, 272 (1984)