I don't know what it is. It's sticking out of my wall. Does anyone have any ideas? It looks like a piece of metal. And lately, I've seen some dampness and water pooling on it a bit. And the area where it is around the floor looks like there is some dampness.
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.
Based on all of the foam and sealant around the object and rust on the floor it seems like the previous owner (or current landlord if you are renting) had an issue which they did not want to address properly.
You can start by cleaning up the object a bit by peeling or gently scraping it until it's more obvious as to what it is or start removing the paneling to see what is being hidden.
The fact that there is water in that vicinity is concerning and you should look into it sooner rather than later.
Per your third picture, the screws holding in the paneling appear to be a square drive and these bits can easily be found at your local hardware store.
Before removing the paneling it would be wise to score the outside and inside corners with a utility knife so that you don't get unexpected paint peeling.