Astronomy: Do I at least understand the basic concept of this?

[Unbiased Laker's Fan]

I have always been confused by Einsteins theory which stated that when we travel at the speed of light we age slower. But now I understand that this happens because when a object moves at or close to the speed of light, its mass increases. And due to the law of inertia, it has more resistance to change...and thats why we age slower.

Or does it have to do with that when we stand near objects with bigger mass's, we experience a slower change of time?

Thanks!