For example, suppose you are standing on the side of a road, with a baseball catcher's mitt.
Standing on the back of a flat bed truck, moving toward you at 40 mph, I throw a baseball to you with, relative to me, a speed of 60 mph. By Newtonian theory, the baseball would have a speed, relative to you, of 60+ 40= 100 mph. By relativity, the baseball's speed relative to you would be very slightly less than 100 mph but the difference would be too small to measure.
If I were to shine a light toward you with, relative to me, speed c, by Newtonian theory, the speed of that light, relative to you, would be c+ 40. But, according to relativity, the speed of that light, relative to you, would still be c. That is what is meant when we say that the speed of light, relative to any observer is c.