The most common use of this word is in "isotropy of space", which is commonly taken as an axiom in mechanics (or physics at large). It means that the laws of physics have no prefered direction, so a mechanical system would behave identically if it were turned some other way.
This is obviously not the case in e.g. a gravity field: things tend to fall towards the floor rather than the ceiling. But when applied to (empty) space, it might seem almost too obvious to deserve mention. A more formal statement of the principle reveals its power: the laws that describe physical interaction in a system does not change if we rotate our frame of reference.
Thus the principle of isotropy of space is a symmetry of the laws of physics. As we know from Conservation laws and symmetry such a symmetry implies a conservation law, which in this case turns out to be the conservation of angular momentum.