How can I temporarily seal a gap underneath my door to stop water getting in while it's raining?
EDIT: Comments above say that you have 1-2" of water.  There is no solution for this other than fixing the drain.  (Or going to marine style doors with a raised threshold.) What I've describe below can mitigate minor flooding, but won't help with the serious issue you seem to be having.  

ORIGINAL ANSWER:

The proper long term answer is to fix the the drain.  However, I appreciate that you are in need of a more short term solution.

In English, what you are looking for is a "Rubber Threshold Seal"  like this:


Or Like This (this is made for garage doors):



Installing these will require drilling through the tile and concrete, installing a plug and screwing it down.  You will also need a liberal dose of caulk (silicone sealer) underneath.

If you're in a real bind, and need a quick and dirty fix until you can get better parts, get a piece of wood, about the width of the door and slightly smaller than the gap, and caulk it down.  Paint it with yellow and black stripes so you don't kick it off.  The sealant won't hold if you stub your toe against it.