Explain pi-base behaviour of Halides in metal complexes?

If you presume that the halogen is sp hybridised. That means it will have two sp hybrids. One forming a sigma bond with the metal and one will be pointing away from the metal.

Then you have two p orbitals left over. These are what normally form Pi-bonds in organic chemistry when you look at Alkynes, with their two Pi-bonds in different planes.

This is what you can think the halogens are doing and they can donate electron density to any d-orbitals that are on the metal which are in an orientation which allows them to overlap. This means they are effectively forming Pi-bonds to the metal.

The same can also happen on molecules in reverse where the d-orbital electrons of a metal can be donated into an empty orbital of the ligand. This is called back-bonding.