What does term "connectivity attributes" mean in AM3359 Cortex A8 processor (used in Beaglebone)?
If you search for "connectivity attributes" in the TRM, each peripheral has a table listing it's attributes. Each table is basically a list of all the signals used to control each peripheral. These tables tell you where each peripheral gets it's power from, which clock signal it can use, the names of its reset signals, the types and names of its interrupt sources, etc.

So in order to use a specific peripheral, you would need to consult these tables to determine which power domain needs to be enabled, which clocks to set and run, which interrupts to enable and write routines for to control the functionality, etc.

In short, "connectivity attributes" are the various sections and signals you need to set and manipulate in order to control a particular peripheral.