fractional coordinates
Where is an atom inside the unit cell? Instead of giving its position in metres, crystallographers give it as a fraction of the way along each cell edge. A point at the very centre is (1/2, 1/2, 1/2); a corner is (0,0,0); halfway along the a-edge only is (1/2, 0, 0). It is like saying halfway across and a third of the way up the tile, independent of the tile's actual size.
A position is written r = x a + y b + z c, with x, y, z each between 0 and 1 (values outside that range simply land in a neighbouring cell). Because they are fractions of the cell edges, the same coordinates describe the same atom whatever the units, and they automatically respect the cell's shape even when the axes are not perpendicular. For example, the two carbons of diamond sit at (0,0,0) and (1/4,1/4,1/4).
The full crystal structure is specified compactly by the lattice parameters plus the fractional coordinates of the atoms in the motif (the asymmetric unit); symmetry operations then generate the rest. Converting a fractional coordinate to a real distance needs the cell parameters — for instance, an atom at x = 1/4 in a cell with a = 4 angstrom sits 1 angstrom from the origin along a.
In cubic CsCl (a = 4.11 angstrom), Cs sits at (0,0,0) and Cl at (1/2,1/2,1/2). To get the Cs-Cl distance, convert: the body-diagonal fraction (1/2,1/2,1/2) corresponds to (a/2) times sqrt(3) = 3.56 angstrom. The fractions stay the same whatever a is; only the conversion uses a.
Fractions describe the pattern; the lattice parameter turns them into real distances.
Fractional coordinates are only unique up to adding whole numbers and applying the symmetry operations: (1/4,1/4,1/4) and (5/4,1/4,1/4) are the same atom in different cells, and symmetry may generate several equivalent positions from one listed coordinate.