This is a bit of a nitpick, perhaps, but the speed of light is contstant in vacuum. Light traveling through matter moves more slowly. So the speed of light in our atmosphere is a little bit slower, and the speed of light in water is slower than that.
Also, if you haven’t studied relativity it may not be clear to you exactly what is meant by “the speed of light is constant”. You might think that if you get in your car and drive down the road at exactly 15 mph, then your speed is constant. But it isn’t constant the way the speed of light is constant. Your car would be moving at 15 mph relative to the road, but at 0 mph relative to you (because you’re in the car moving with it.) The speed of light, however, has the same constant value in every inertial (i.e. unaccelerated) reference frame. That is to say that if I’m “standing still” on the earth watching a beam of light fly by, and you’re chasing after the beam at 1/2 light speed, we’ll both see the beam moving away at roughly 300 million meters/second, even though common sense tells you that you should see it moving at half that speed. This bizarre fact gives rise to all sorts of disagreements about our measurements of distances and time intervals and such.
However, these differences are only really noticable if one of us is moving at a significant fraction of light speed, as in the above example. In normal day to day life, you might be driving along at as much as, say, 80 mph relative to me, but this is still insignificant next to the speed of light, and the differences in our perceptions are too small to be noticed.
I hope this makes sense. I’m sure if I’ve made any errors in this explanation, someone will correct me.