In the early days of serial communications buffered UARTS were not really necessary. This is because all operating systems were not multi-tasking, I.e. in DOS for example you did not edit text and communicate simultaneously.
With the advent of Windows and other multitasking operating systems it became necessary to both edit (using a word processor) and communicate simultaneously. This meant that incoming data could be missed if a document was being edited.
A buffer is an area of memory in the UART in which to store incoming data. It allows data to be stored physically in the UART which can later be serviced by a software driver.