Fuel systems are in general fed by gravity, at least until the fuel leaves the tank, where sometimes (always if the tank is lower than the engine) a pump pushes it toward the engine. This means that fuel is generally extracted from the bottom of the tank (or slightly above the very bottom to avoid having small particles from the bottom of the tank clogging up the fuel filter, incidentally this also introduces the concept of
unusable fuel, as the stuff remaining at the bottom of the tank, although there are a lot more factors to this).
Fuel is less dense than water, meaning it'll float on top of the water. Or if you want to think of it the other way around, water is heavier and will sink to the bottom, right where you're trying to get your fuel to feed to the engine. Water doesn't burn very well and the engine will stop. Avgas is generally 0.72 kg/l and Jetfuel around 0.82 kg/l (water being 1 kg/l, see have SI units work well that way?).
A tiny amount of water probably mix with the fuel and simply reduce the power output slightly, whereas anything more will be drained from the tank first, and it'll be very hard to restart the engine. You'd have to pump all the water through the cylinder and out the exhaust, and I don't think this is generally possible in flight, especially right after takeoff which is generally the case when you have water in the fuel (could be right after switching tanks too though).
I don't know much about turbine engines, but I suspect they're less susceptible as the water will not prevent relighting the engine (the pumps will simply push the water out, there's no cylinder that could fill up with water), and you'll generally be using up more fuel on the ground making the problem readily apparent. This is pure speculation though.