A switch fabric interconnects the port ASICs of a switch to allow transmission of data and control signalling. A fabric can be built-in (as it is on most of the non-modular switch types you mention) or externalized into one or more separate modules - as it is on a large modular core or data center switch such as a Nexus 7k or 9k series.
When the switch is a modular type (i.e., with linecards inserted into a chassis), the backplane (or midplane depending on the architecture) is the physical set of connections that allow signals to travel among the cards.
When you have an entry level switch such as the 2960, it only has a single port ASIC internally and thus does not need either a fabric or a backplane.
Please refer to one of the Cisco Live presentations for a more in depth explanation. For instance, "BRKARC-3437 - Cisco Catalyst 3750 / 3560 and 2960 Series Switching Architecture (2013 Orlando)"
