An outer orbital complex uses "d" orbitals from the (n) shell to form "sp"^3"d"^2 hybrid orbitals for bonding.
Inner orbital complexes
["Co"("NH"_3)_6]^"3+" is an inner orbital complex.
The electron configuration of "Co"^"3+" is "[Ar] 3d"^6.

The "3d, 4s" and "4p" orbitals are close in energy, so the ion can easily form six "d"^2"sp"^3 hybrid orbitals for bonding to the "NH"_3 ligands.
This is an inner orbital complex because it uses the "inner" "3d" orbitals for bonding.
Outer orbital complexes
["CoF"_6]^"3-" is an outer orbital complex.

Here, the empty "4s, 4p" and two of the "4d" orbitals can form six "sp"^2"d"^3 hybrid orbitals for bonding to the "F"^"-" ligands.
This is an outer orbital complex because it uses the "outer" "4d" orbitals for bonding.
For an excellent explanation of inner and outer orbital complexes, see this Socratic answer.