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.
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.