POD stands for "print on demand" (never "publish on demand"—that's a meaningless term favoured by vanity presses). It uses digital technology to print books one copy at a time, in direct response to demand. It has its advantages: setting it up is quick, simple and (usually) free, and it allows small publishers to operate without incurring large printing costs. However, the cost per book never varies: whether you print one copy or one thousand the cost per book remains the same, making it impossible to exploit economies of scale. The physical quality of most POD books is not brilliant: curling covers and loose pages are commonplace, although this is improving. POD services are accessible to anyone with access to the internet via websites like Lulu and cafepress, which has led to a vast increase in the number of books being self-published (most of which are dire), and a vast increase in the number of small publishers setting out their stalls (not all of them with the expertise to succeed).
Offset printing (also known as offset lithograph, or litho, printing) requires big, expensive machines, a complicated setup, and expert staff to manage the whole process. Although the actual cost of printing each book is low, the setup and clean-down cost per print-run is high and fixed. While it would be possible to use offset to print a single copy of a book, those fixed setup costs would then have to be borne by that single copy, which would be uneconomic. However, if several hundred (or thousand) copies of that book are printed in one run then the overall cost per book drops dramatically, and becomes lower than using POD. Add to that the higher quality which offset delivers, and it becomes obvious why big publishers stick with offset. Prior to POD, it was the only printing option available to self-publishers: in an effort to keep their unit costs realistic many self-publishers over-ordered, and ended up over-stocked and cripplingly out of pocket.