What is an aviation handler?
Handlers are private companies who provide services (for a fee) to pilots and passengers when they fly in and out of an airport.

Depending on the airport, sometimes handlers are required by the local authorities to be used, and other times there are not even any handlers available (a lot of US airports do not have them, for instance).  Often though, they are optional and there to assist crews that are unfamiliar with the procedures at a new airport or who want their assistance as a convenience.

They typically assist with coordinating things like fuel, lavatory service, flight plans, local permits, passenger transportation, catering, coffee/ice/newspapers, etc.  Many times they pay for everything (in the local currency) and provide one consolidated bill for the client to pay.

Note that handlers can be employed by local FBO's (Fixed Based Operators), or they can be part of a larger international company that provides handling services all over the world.  In either case, they are generally coordinating all of the different parties and services needed in order to operate an aircraft in and out of their airport.