Coordination isomerism arises in compounds where both the cation and anion are complex entities. It involves the interchange of ligands between the cationic and anionic coordination spheres of different metal ions.

In the given example:

1. In $[Co(NH_3)_6][Cr(CN)_6]$, the ammonia ligands are bound to Cobalt ($Co$) and cyanide ligands to Chromium ($Cr$).
2. In its isomer $[Cr(NH_3)_6][Co(CN)_6]$, the ammonia ligands are bound to Chromium ($Cr$) and cyanide ligands to Cobalt ($Co$).

Since the ligands ($NH_3$ and $CN^-$) have been interchanged between the two metal centers, this is a classic example of coordination isomerism .