What are the three copper connections to my water heater?
Depending on the specific system installation and type of tank it could be any of these:


Cold in, hot out, and overflow:  Standard water heater.
Cold in, hot out, recirculate in.  This configuration has diverse uses:


typical for a solar water heating booster.
In heavy use applications, it could be for an external hot water reservoir.
In long lines applications, this could be for recirculating hot water so that a faucet 400 feet away has hot water available just a few feet away.  Many motels and hotels are plumbed this way.