a slip system
A dislocation cannot glide just anywhere or in any direction — it slides on a particular plane, and along a particular direction within that plane. Pair those two together — one slip plane plus one slip direction lying in it — and you have a slip system. It is the complete answer to the question, on what surface and which way does this crystal shear? A crystal usually has several equivalent slip systems by symmetry, and how many it has, and how they are oriented, decides how readily and in which directions the crystal can be plastically shaped.
The rule for both halves is the same: pick the easiest. The slip PLANE is the close-packed plane (widest spacing, smoothest sliding), and the slip DIRECTION is the close-packed direction lying in that plane (the shortest Burgers vector, along which atoms are packed touching). In face-centred-cubic metals this gives {111} planes with <110> directions; each of the 4 distinct {111} planes carries 3 close-packed <110> directions, so there are 4 times 3 = 12 slip systems. Body-centred-cubic metals slip in <111> directions on {110}, {112} and {123} planes, offering 48 or so systems but each harder to activate; hexagonal close-packed metals often have just the basal (0001) plane with 3 <11-20> directions — very few systems.
The count of slip systems has real consequences. Von Mises argued that to change shape freely a polycrystal needs at least five independent slip systems; FCC metals like copper and aluminium have plenty and so are famously ductile, while HCP metals like zinc and magnesium, short on easy systems, are more brittle and must call on twinning or harder secondary systems to deform. When a single crystal is pulled, the slip system that switches on first is the one with the highest resolved shear stress along it — captured by Schmid's law — which is why the same metal yields at different applied stresses depending on its orientation.
FCC aluminium: 4 close-packed {111} planes times 3 close-packed <110> directions each = 12 slip systems, e.g. plane (111) with direction [1-10]. That direction lies in the plane (check the dot product: (1)(1)+(1)(-1)+(1)(0) = 0, so [1-10] is contained in (111)). Plenty of systems means many independent shear modes, which is why aluminium is so ductile.
Slip system = close-packed plane + close-packed direction in it; FCC has 12, HCP often only 3, which sets ductility.
A slip direction must lie IN the slip plane — the two are not independent choices. A common error is to pick any low-index plane and any low-index direction; only the plane-plus-direction pairs that satisfy this, and are close-packed, are the real active slip systems.