You can attach one rigidbody object to another or to a fixed point in space using a Joint component. Generally, you want a joint to allow at least some freedom of motion and so Unity provides different Joint components that enforce different restrictions.
For example, a Hinge Joint allows rotation around a specific point and axis while a Spring Joint keeps the objects apart but lets the distance between them stretch slightly.
2D joint components have 2D at the end of the name, eg, Hinge Joint 2D. See Joints 2D for a summary of the 2D joints and useful background information.
Joints also have other options that can enabled for specific effects. For example, you can set a joint to break when the force applied to it exceeds a certain threshold. Some joints also allow a drive force to occur between the connected objects to set them in motion automatically.
See each joint reference page for the Joint classes and for further information about their properties.