Plumbing

This is more of an electrical problem rather than a plumbing issue. But rust inside the junction box is a sign of water getting into it. You need to find the source of the water that's getting in and stop that too. It looks like there is only a bad connection inside the wire nut. Most likely due to being wet. You can try changing the wire nuts if you feel comfortable with electricity.

1. Switch the breaker to "off" and lock it out & tag it so nobody turns it on accidently.

2. Verify power is off to both wires with a meter or voltage indicator.

3. Cut back the wires until you have a good section of wire to strip and install new wire nuts. (Remove one wire nut at a time so you don't mix wires.)

If you are not comfortable with electricity please do not attempt this repair and contact someone who is.

Call an electrician,

You clearly have a short somewhere.

All I can tell from that photo is that the wire nut has overheated and at a minimum the wire nut needs to be replaced. More may need to be done depending on why it overheated. If it was simply a poor install of the nut to begin with, replacement may be all that's needed. If there is something else going on causing high current draw hence overheating, you'll need to troubleshoot that too

You have what is called an electrical short to ground.

You need a professional.

This is caused by excessive current traveling straight to ground. Which in turn causes the point of highest resistance to become very hot. Which in turn increases the resistance of that point in a sort of runaway effect of increasing heat and resistance. Until you reached the flash point of the material.

Changing the wire nut will not solve the problem. It was only an indication of a problem.

Thanks all who replied. I ended up investigating some more and noted that the wires inside the nut that melted were barely connected. I checked the elements resistance in the water heater and visually checked the electrical wire going to the breaker box. Everything looks clean with no indication of an issue besides that wire nut. I'm concluding it was a loose connection and hoping that is right. I redid the connection and installed a fire alarm right above the water heater. I then let the water completely warm up and checked the wires (after turning off power) to make sure they were not hot. So far it is all working as expected.