When we say that everything can be made from NAND gates, we really aren't kidding. You can use NAND gates to make NOT, AND, OR and NOR gates. And even some other basic things....
If you can't see the simulation below, try this HTML version of the Falstad simulator: Make all Logic from NANDs
The RS Flip Flop: How computers learn and remember. Or XOR, XNOR which detect Different or Equal?
Of course, these gates aren't really made of NAND gates in the actual computers. They are made from transistors, resistors, and diodes.