Intels First serious attempt at making a low-cost CPU for the masses. The 386SX was funtionally on par with the better 386DX, except for the most important reason: The 386DX has a 32-bit internal and external path, while the 386SX uses the slower (but cheaper) 32-bit internal path with a 16-bit external path. While there were other changes as well, like power consuption and die size, the data pathway issue was the most important.
While it was harder from a technical standpoint to make a chip that concentrated it's bit path down that far, Intel took the gamble because, with a 16-bit external path, much of the chipwork designed for the 286 would would with the new 386SX -- in fact, many later 286 and 386SX motherboards were identical except for some minor differences like the socket size and clock chip. It would also only require memory banks that where 16-bits wide instead of 32-bits so as to be easier for consumers to afford.
The SX Line was late evolved by IBM into the 386SLC line, an SX that used Static Field Transitors to dramatically reduce power consuption, for use in laptop computers.