A polymer melt can be compared to a plateful of spaghetti: lots of long flexible chains mixed and entangled with each other. Every one of those long flexible chains, a polymer molecule, can be represented by a bead-spring element.
The spring simulates the non-linear elastic behaviour of the material, which should therefore be a non-linear spring. Like in a plate of spaghetti, the bead-spring elements (or polymer chains) slide over each other, which simulates the non-linear viscous effect.
On imposing a deformation, the molecules stretch and orient. The spring, representing the elastic part of the material, forces the material to return to its equilibrium state. However, the molecules are meanwhile slipping or sliding over each other, representing the viscous behaviour of the material. This makes the material to be unable to return to its initial equilibrium state, which it seems to have 'forgotten' and the material will try to return to a new equilibrium state.
Although polymeric materials do not have an actual memory, the previous described effect is often referred to as 'fading memory'.