OK, let me see if I can get very layman and not use the technical words.
Relative = in comparison to
Imagine you are at the airport with a friend, John, where they have those funky travellators for people who don't want to walk very far.
You and John stand next to each other. Relative to each other, you are not moving. Relative to the rubbish bin next to you, you are not moving either.
You and John get on a travellator together and stand still. Relative to each other, you are not moving. Relative to the bin you are now moving away from it at travellator speed.
You have some time to kill before your plane goes, so you jump on a travellator going North and John jumps on the travellator going South. Relative to the bin you are both moving at travellator speed. Relative to each other, however, you are travelling at twice travellator speed.
OK, now going to your point. If we want to assume that the speed of light is constant at c, then in the last example, where you and John are travelling at twice the speed of the travellator, relative to each other, then we have to explain it another way.
To the rubbish bin you are travelling at travellator speed, c, and to each other you must be travelling at travellelator speed, c. SO what must be different when you look at John and he looks at you? It must be the other stuff, length and time: v= d/t
That pretty much says what everyone else has said, so I hope it has helped.