An autologous transplant is a transplant of an organ or tissue that is taken from the same individual who receives it.
A person having blood taken a little at a time several months before a surgery to replace the blood he or she expects to lose during that surgery is creating an autologous transplant. Likewise, the use of muscle tissue taken from a person's back to surgically reconstruct their damaged hand would be receiving another form of autologous transplant. So would a woman having a breast reconstructed after a mastectomy via fat tissue taken from her own thigh.
The information in this writeup was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entry this is based on.