The word prim is a shortened version of "primitive" and refers to the 3D polygonal shapes used by residents to build objects in Second Life. Commonly used primitive shapes are cubes, spheres, and cylinders which can all be "linked" together to form more complex objects. Other types of prims are prisms, tori, rings, and tubes. Prims can be edited in a multitude of ways (parameters/properties): scale, cut, hollow, twist, dimple, shear, skew, revolve, radius delta, set physical, made flexible and/or a light, and more.
A single prim is also an object type of item and will be represented as such in a resident's inventory (being placed in the "Objects" folder with an object icon) but, typically elsewhere in SL's UI, an object refers to a full linked set of prims.
Back in the early beta period of SL, there was a prim type called a "spiral" (which may have looked similar to the cork-screw shape that can be made with rings) that was removed due to its impact on the physics engine. Tubes were also removed for a period of time.