A mortise and tenon joint is one of the most basic and strong ways to join two boards together, but it takes a bit more time (and more tools) than some joinery techniques.
This video is a great overview of mortise and tenon joints and how to make them using several different types of tools, including a router, hollow chisel mortiser, and table saw. If you're more inclined to use hand tools, here's a great video on how to mark, cut and chisel a mortise and tenon joint by hand.
A mortise and tenon joint is most often used in applications like bed and table frames, or when constructing windows, doors, or the face-frames of cabinets.
Review of Mortise and Tenon Options [The Wood Whisperer]