We will need a better photo. This one is too blurry. We will need a room shot and then a slightly better close up.

How old is the floor?

I'm guessing that is vinyl, vinyl tiles or sheet vinyl. Stains get on vinyl and don't come out. The solution is to replace the flooring.

More likely the stain is under the floor. And you're right, it is horrible, but not because of the stain. A shower should never flood the floor surrounding it. You need to pull that vinyl up and look at the floor underneath. I'd be willing to bet it's heavily damaged. Look at the wall, it's all bubbled up, that should have been your first red flag.

suedonim probably had it right. Those stains most likely caused by water and are under the floor. Fix the water issue and replace the tiles.

You can't let water come out of the shower onto the floor, especially repeatedly. Either you need to find someone to repair it, or if you rent insist your landlord repairs it. And I'd assume the floor and what is below the linoleum is going to need replacing if this has been happening for awhile.

What is worse, is that letting this continue, definitely leads to mold problems, that than can affect your health.