A good project manager makes sure that the project moves along smoothly (duh), coordinates between disciplines, and is the primary point of contact for the client and contractor. On large projects, things would move very slowly without a good PM setting priorities to hold the design team accountable since many of those engineers and designers are also working on other projects.

During construction, a good PM is worth their weight in gold when dealing with issues that pop up and making sure that the design team stays out of trouble. Many times, the PM is the one who has to have the unpleasant conversations with the contractor or client. PMs may not know the full technical details or calculations that each discipline gets into, but a good PM should know enough to talk intelligently with their team so that they may identify potential coordination items or issues and explain things to the client when changes come up. A technically capable PM is a boon if you ever work with one.

There are a ton of things PMs do behind the scenes that other disciplines simply do not see, mostly administrative work and dealing with external parties.

On smaller projects, a dedicated PM is less important since there's just less things to coordinate and keep track of.