Load Arduino flash code from SD card
See topic #16812, “Load sketch code from SD Card”, in forum.arduino.cc, which explains how to replace the ordinary Arduino bootloader with one that can load programs from an SD card.

Also see Bootdrive loads Arduino sketches from SD card at dangerousprototypes.com, which gives different code to do the same thing.  It also mentions BootDrive for Arduino from baldwisdom.com.

Note, the program code that these loaders install into flash is already compiled, as opposed to being original C source code.  If you want to load source-level code into the Arduino, look for an interpreter / interpretive language to run on the Arduino.