A free quark is a quark that is not bound to another quark (or, in general, not part of a color-neutral) group. A free quark could be identified by its distinctive fractional electric charge. However, searches for free quarks have consistently come up negative.
The color force becomes stronger as the distance between quarks grows larger. Eventually the work done separating the quarks becomes enough to create a quark-antiquark pair. These will combine with the original quarks to form two color-neutral groups. So one always finds (when splitting quark groups) a new quark group instead of a free quark. This phenomenon is known as confinement.
See also:
Confinement