Most "plastics" are polymers that are long enough to be held together via chain entanglement. The polymer chains are long enough that the are tangled up (oftten times this is described like a bowl of spaghetti). This increases the viscosity of a polymer. When the material is below the Glass Transition Temperature (Tg) it is then hard and generally doesn't flow.
Other factors can affect the mechanical properties such as crystallinity, chain structure, etc.