The original crossbar can be seen in old movies where there was...

The original crossbar can be seen in old movies where there was a switch operator for connecting phone calls.
The operator would draw a lead from an array of sources (callers) and connect it to the phone socket line for the intended recipient.
The idea of a crossbar is retained for implementations of getting from one place in a row and column of an m by n matrix to another place in the matrix, eg for matrix multiplication.
Those involved in Ai have taken up the idea in propagating signals across cells in a matrix layout.
It is better to look behind the word "crossbar" to the actual implementation.