Try to think of how the water flows in your system...
The water comes into your water heater on the bottom from the cold/blue line.
The WH fills and heats the water. Hot water exits the tank from the top hot/red line.
When you want hot water, you open a hot faucet but for hot water to get to that faucet, additional cold water has to enter the tank and 'push' the hot water to the faucet.
The hot and cold valves have to be open for this to happen but also, the bypass valve has to be closed. If the bypass valve isn't closed during normal operation, the cold water will not be able to exclusively 'push' the hot water from the tank because two lines are now connected to each other. The cold water will simply mix with the little bit of hot water coming out of the top of the tank.
I said all that so you understand why two of the valves are open and one is closed as in your photo. You questioned why the hot and cold were open and the one to the right was closed. Hopefully now you know why.
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