So, what have we established? We've established now that the speed of light is invarient for all observers/reference points. This is included in the second postulate of the Special Relativity Theory (SRT). The first postulate, as we went over, is that for all frames of reference, the physical laws of the universe are the same.
Let us say that two objects moving through space are A and B. A is travelling at 1/2 the speed of light towards object B. A emits light. We might therefore expect the light emited by A to have a total velocity of 1 1/2 the speed of light. The second postulate of SRT says "NEIN!" The light emited by A is still only going the speed of light, c. However, according to an observer at A, the light emitted by A is also going the speed of light! This is weird behavior. If A was instead going 5 miles an hour and threw a softball 1 mile an hour, the softball would be going 1 mile an hour from the perspective of A, but 6 miles an hour from the perspective of B. It really wouldn't matter if A was going 5 miles an hour, 1/2 c, or 9/10 c, the difference in these two situations is that one is dealing with a 1 mile an hour softball and the other is dealing with the speed of light. But again, according to the first posulate of SRT, are they really that different? And now hopefully we see the complication.
The true difference in the 1 mile an hour softball and the speed of light in my examples is only a matter of scale. The same laws and effects are in play, the only difference is that the effect is unappreciable at the slower speed of the softball scenario.
I mentioned consequences of this earlier. There's more consequences to this and I'll be going over them in a bit.