hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation: all other translations or rotations being prevented, and thus it has one degree of freedom. They may be made of flexible material or of moving components. In biology, many joints function as hinges like the elbow joint.

There are many types of door hinges. The main types include:

Spring hinge
a spring-loaded hinge made to provide assistance in the closing or the opening of the hinge leaves. A spring is a component of a it, that applies force to secure a it closed or keep it opened.
Barrel hinge
a sectional barrel secured by a pivot. A barrel is a component of a it, that has a hollow cylinder shaped section where the rotational bearing force is applied to the pivot, and may also have a screw shaped section for fastening and/or driving the pivot.
Pivot hinges
which pivot in openings in the floor and the top of the door frame. Also referred to as a double-acting floor hinge. This type is found in ancient dry stone buildings and rarely in old wooden buildings. These are also called haar-hung doors. They are a low cost alternative for use light weight doors.
Butt/Mortise hinges
usually in threes or fours, which are inset (mortised) into the door and frame. Most residential hinges found in the U.S. are made of steel, although mortise hinges for exterior doors are often made of brass or stainless steel to prevent corrosion.
Case hinges

Case hinges are similar to a butt hinge however usually more of a decorative nature most commonly used in suitcases, briefcases and the like.

Continuous hinges, or piano hinges

This type of it is also known as a piano hinge. It runs the entire length of the door, panel, or box. They are manufactured with or without holes. They  also come in various thicknesses, pin diameters, and knuckle lengths.

Above info is from the reference.