Does anyone know what this metal thing in the corner of my basement is?
It looks like you have a basement laundry room with cinder block walls.  The vertical structure doesn't look like metal to me, more like fiberboard put up to hide a soil stack and other plumbing.  With the shampoo and wash cloth hanging on the utility sink... Do you have a shower down there too?

Either the plumbing hidden behind the fiberboard wall may be leaking or the humidity from laundry or a shower may be condensing on the wall or whatever's behind the fiberboard, then soaking through from behind and puddling on the floor.

To figure out what's really happening you'll probably have to unscrew the fiberboard and look behind it.  If it's a leak, fix it.  If it's condensation, there are several ways to address it depending on how much effort and expense you're willing to go to.