So many incorrect methods in the comments.

It's egg yokes, mixed with the rendered fat from cooking the Guanciale. Add the cheese (Pecorino traditionally, but I like a bit of Grana Padano mixed in) then add a little bit of pasta water to get the right consistency. Add generous black pepper to taste.

Use a double boiler for mixing if your arms need a workout, or a blender if lazy.

Edit: None of you snobs know how to cook....lol. Guess what...you can use a blender to make the sauce for Cacio e Pepe as well.