As the CPU and the peripherals can be in different clock domains, that is, they are clocked from different clock sources and with different clock speeds, some peripheral accesses by the CPU need to be synchronized. In this case the peripheral includes a Synchronization Busy (SYNCBUSY) register that can be used to check if a sync operation is in progress.
For a general description, see Register Synchronization. Some peripherals have specific properties described in their individual “Synchronization” sub-sections.
In the data sheet, references to Synchronous Clocks are referring to the CPU and bus clocks (MCLK), while asynchronous clocks are generated by the Generic Clock Controller (GCLK).