In the context of Space Time Coding, full diversity refers to the fact that each transmitted symbol will experience all the independent paths in the system to the receiver. In other words, you have M transmit antennas and N receiver antennas and assume all pair-to-pair channels are independent, then your codebook (the coding matrix at transmitter) will have the property that each symbol will be transmitted through all transmit antennas (you will find a symbol, say, s1, appears in every row of the matrix). Thanks to this design principle, the symbol error rate has the form of 1/SNR^{MN} at high SNR. This is the strict defintion of achieving full diversity.