SPI stands for Serial Peripheral Interface. It's a bidirectional clocked serial interface that's popular for many small devices.
Serial Peripheral Interface Bus - Wikipedia, the free encyclopedia
It's not very difficult to interface with it using an 8051 with software SPI code. If you want more information on the 8051 simple use Google, there are oodles of code for the 8051 out there. The hard part with accessing an SD card is managing the file system, there's a lot of code required for that if you want read/write access. Simple read access is a little easier.