What is reverse transcription?

"Transcription", in the sense of DNA, is the process whereby DNA is used as a template to synthesise a new strand of RNA. (This RNA can then later be translated into a protein.) So, transcription is DNA → RNA.

Reverse transcription is (as the name suggests!) the process reversed. (Single stranded) RNA is back-translated into (double stranded) DNA; i.e. RNA → DNA.

What function does this have in the human body? Well, none. It isn't a normal occurrence in humans. It turns out that the only things that naturally do this are certain viruses - retroviruses, specifically. They have an enzyme called reverse transcriptase that does most of the heavy lifting in this regard.

HIV is the standard example of a retrovirus. Once it gets within our cells, its RNA is converted to DNA, which is then inserted into our genomes. From there, HIV's genes are expressed (transcribed and then translated) in the normal manner - which is bad for us.