Well, this exact same problem happened before, which was the reason my whole bathroom got torn up. I flushed, noticed water leaking from under the toilet, called the plumbers. (Which then turned into a whole thing as it revealed other problems.)
They said the water leaking through the seal was because the floor and supports under the toilet had weakened (rotted), causing the toilet to sink into a depression in the floor (which it was.) This cracked and broke the original seal, which allowed water to flow under the toilet and on to the floor. So they tore up the floor, put in new supports, got the toilet seated level, put new flooring on, put the toilet on and sealed it.
But since the same thing is happening again, I don't fucking know anymore. The plumber said he upped the amount of water going into the bowl, to help it flush with more force to prevent future clogs. So maybe there's too much water flushing now and it's over flowing somewhere inside the toilet, leaking out to the floor and creeping out under the (poorly done I guess) seal. I'm not a plumber either. But I do know that this is all BS and neither I nor my landlord should be paying a dime on this. 3 fucking people have looked at this toilet now a total of 6 times, so there's no fucking excuse for no one catching whatever the problem is here. And it worked perfectly well from the time the work was finished until this dude (who has been the same dude through every single visit) touched it. And all he did was snake the drain, and increase how much water is flowing to it. And all I did was flush it three times in a 4 minute period.
All I can say is, I'm glad I haven't paid a dime on this bathroom. Because all told, it and all its associated problems have already run my landlord close to a grand or more, after insurance. And like I said, I've only been here 5 months.