A quark is fundamental particle which participates in the strong nuclear force. The theory of quarks is know as Quantum Chromodynamics or QCD. All hadrons are comprised of quarks, in particular, the atomic nuclear constituents, protons and neutrons, are composed of 3 quarks each. Pairs of quarks also comprise mesons, such as the charged and neutral pions.
Quarks are never observed in isolation, only in pairs or triplets. This is due to the fact that the strong force that affects quarks increases with distance: not unlike a elastic string, as 2 quarks are moved farther apart, the force between them increases. At a certain point the force between the quarks is so strong - there is so much energy in the force field between them - that the 'string' snaps, and a quark anti-quark pair is created by that energy.
Quarks come in 6 flavours or species, with the rather poetic names:
|up, u||charm, c||top, t|
|down, d||strange, s||bottom, b|
A proton for instance is composed of uud quarks, whereas a neurton is composed of udd quarks. The large number of quark combinations leads to a particle 'zoo' being observed, with properties in agreement with QCD. Also, much like electrons and protons have 2 charges, positive and negative, quarks have three 'colours' (the name 'colour' is just a label like 'charge' to represent this property, but has nothing to do with colour as we know it):
Like all fundamental particles, for each quark, there exists a corresponding anti-quark with opposite quantum numbers; there exists, for instance an ū or anti-up quark with opposite charge. Mesons are composite particles composed of pairs of quark/anti-quarks. For example the three pions observed are π- π0 π+, and are composed of respectively dū, (uū - dƌ)/√2, and uƌ.