What is this silver plate beside by tub and what is it for? Why is it leaking? What to do?
That's a cover for your drain clean out. If water is leaking out of there then either the threaded cap below, if there is one, is loose or there is a blockage starting to form and the drain water is starting to backup because it can't go down the drain fast enough. There could also be a drain plug under the cover that has deteriorated and is leaking. You can undo the screw on the cover and check it out and see what the problem is. Take some pictures. Then come back here for some solutions. Here's what the drain plug would look like.