I am updating my electrical outlets and switches. I noticed on many of the metal boxes there is always a ground wire clipped to the box but also one connected to the fixture. What is the purpose of the one clipped to the box? Is it necessary? A clip was broken so I removed the wire for now and am wondering if I need to get the proper equipment to repair.

Insulation breakdown can energize the box. The clips help detect insulation and/or component breakdown. A hot wire that say accidentally slips out of a wirenut would touch the side of the box will blow a fuse rather than energise the fixture. You should be able to see this effect better with a light fixture.

Suppose the box wasn't grounded and the hot touched the side of the box. The unsuspecting person would try to change a light bulb and get shocked.

The grounding is also part of the equipotential system in the house. It will assure that plumbing fixtures, electrical fixtures and appliances are at the same voltage to one another.

The clips are readily available. Installation can be a pain, but is typically done with a screwdriver. I install them by hitting the end of a screwdriver on the clip.

It's difficult to guarantee that the ground on the outlet will provide a good connection to the box, hence the box must be done separately.

It is to protect your safety when electric circuit has short current or wire broken. The grounding line will earthing your metal box, then circuit breaker will jump to secure your safety.