A mortise and tenon is an extremely sturdy and strong way to join wooden furniture. A recess is created in one member (mortise) that allows a protruding tongue from the other (tenon) to fit tightly inside. There's no better way to assemble table bases, chairs, benches, and even frames.
Except, mortises can take a serious amount of work to cut. Unless you have a dedicated mortising machine, you're in for lots of time with a chisel and mallet, especially on large mortises like the one shown above.