The teat cup you see on a cow during milking is actually two parts working together: the flexible rubber liner that directly touches the teat, and the rigid shell around it that houses that liner and creates the sealed vacuum chamber the pulsation cycle depends on. The Teat Shell is that outer casing — typically stainless steel, built to hold its shape and withstand daily handling far longer than the liner inside it needs to.
Because it's rigid rather than flexible, it doesn't wear from flexing the way a liner does, so it's replaced far less frequently — usually only when it's dented, corroded, or damaged in a way that compromises the airtight chamber it needs to maintain around the liner. A dented or deformed shell can prevent the liner inside from collapsing and opening correctly during the pulsation cycle, even if the liner itself is brand new — which is why the two need to be considered together when something's not milking right.