A dado (US Canada) Housing (UK) trench (EU). A through dado is when the cut passes completely through the surface, while a blind or stop dado ends before one or both of the cuts meets the edge of the surface.
May be combined with rabbit and tongue joins to create more complex connections
Cut perpendicular to wood grain (to avoid breakouts)
Commonly found in shelf units (bookshelves/cases)
Can be cut by table saw or router. Or by chisel if you are skilled.
Avoid cutting more than 1/3 of the way through the stock receiving the dado to prevent weakening of the joint.