Why is my water expansion tank leaking?
A water expansion tank gives water a place to expand in a closed system (frequently found with boilers, or home water supplies with a check valve). Otherwise, heated water cannot expand and instead increases pressure until some component of the system leaks or explodes.
If the tank is on the hot water heating system, then it's there to relieve expansion from the water being heated. I can't tell from the photo if it's on the heating system or on the home water supply.
Leaks tend to travel down with gravity, if you see evidence of a leak above the tank, then it's likely at the top of that evidence, not the bottom. Shutoff the water, find the source of the leak, and replace the problem area. It may be as simple as needing to unscrew a threaded connection, clean the threads and apply pipe dope, then tighten everything back up. But with visible damage, you'll likely need to to replace the problem area with new pipes.