A bit late though, I'll answer anyways.
Computing Slot. Can you think of all the various computations in the Hadoop that would require some resource i.e. memory/CPUs/Disk Size.
Resource = Memory or CPU-Core or Disk Size required
Allocating resource to start a Container, allocating resource to perform a map or a reduce task etc.
It is all about how you would want to manage the resources you have in hand. Now what would that be? RAM, Cores, Disks Size.
Goal is to ensure your processing is not constrained by any one of these cluster resources. You want your processing to be as dynamic as possible.
As an example, Hadoop YARN allows you to configure min RAM required to start a YARN container, min RAM require to start a MAP/REDUCE task, JVM Heap Size (for Map and Reduce tasks) and the amount of virtual memory each task would get.
Unlike Hadoop MR1, you do not pre-configure (as an example RAM size) before you even begin executing Map-Reduce tasks. In the sense you would want your resource allocation to be as elastic as possible, i.e. dynamically increase RAM/CPU cores for either MAP or a REDUCE task.