Physicist: That is such a hard question. Holy crap.
If you kept the laws of the universe the way they are, but ramped up the speed of light to infinity you’d end up with a surprising array of effects. Newton would have been right about a lot more (nicely done, old dude), there would be no magnets of any kind, the amount of energy tied up in matter would also be infinite (E=MC2) so you’d have to be extra careful not to bring it near anti-matter, but not too careful because anti-particles probably wouldn’t exist (probably). Also, all the weirdness of relativity would be out the window.
But, why is the speed of light finite? I don’t know. I think this is one of those culdesacs of science. It is what it is.
The question, as it was originally asked, was about what keeps light from going any faster. The answer to that question is that there is no faster. If you shove a stone of mass X and it goes flying off at speed V, then if you shove a stone of mass X/2 it’ll fly off at speed 2V. So, you might suspect that if you shove a stone of zero mass that it would go flying off at an infinite speed.
Well, that’s pretty much what photons (which have zero mass) do. If you think of infinite speed as how fast you’d be going if you accelerated forever, then the speed of light is exactly that. If you got into a rocket that could accelerate forever (using some kind magic fuel, such as the Schwartz), and you let it run for an eternity or two, then you’d be moving at the speed of light.
So it’s not that there’s anything slowing light down, so much as the laws of the universe are such that it doesn’t really make sense to talk about something moving faster. More here:
Also, if you’d like to find more “culdesacs of science” get yourself a toddler during their “Why?” phase, and try explaining something to them.