Local resources are locally available computational resources, specifically the number of hardware threads and the number of GPUs.
An allocation enumerates the computational resources to be used for a simulation, typically a subset of the resources available on a physical hardware node.
New users can find using contexts a little verbose. The design is very deliberate, to allow fine-grained control over which computational resources an Arbor simulation should use. As a result Arbor is much easier to integrate into workflows that run multiple applications or libraries on the same node, because Arbor has a direct API for using on node resources (threads and GPU) and distributed resources (MPI) that have been partitioned between applications/libraries.
An execution context contains the local thread pool, and optionally the GPU state and MPI communicator, if available. Users of the library configure contexts, which are passed to Arbor methods and types.