These two terms refer to a printer's capability to print on both sides of a sheet of paper. A duplex printer has a unit attached to it that after printing the even page turns the sheet upside down and resubmit it to print the odd page, thus printing two pages on one sheet; this can save a lot of paper.
A simplex printer simply outputs the sheet of paper after printing a page, but this doesn't mean that it cannot print on both sides as well, although not automatically (see also Q13).
Q13:
How can I print a PDF document in duplex format with a simplex printer?
A:
If you have Adobe Acrobat Reader version 4 (or above) installed, it's easy. Print the odd pages first, turn the printed paper stack upside down, put it into the paper tray and then print the even pages. If you have a printer that prints on the bottom side of the paper you may want to print reversing the page order.
If you have a previous version of Acrobat Reader or just don't have it, then download the latest version. It's free.