In 1905, Einstein published what is now called special relativity. We have the famous E = mc^2 as well as some other results: time slows down with speed, lengths get shorter with speed, and mass increases with speed. If it helps, the idea of mass increasing makes sense straight from E = mc^2. If an object moves faster, the total energy increases since there is more kinetic energy. So the left side increases. This means the right side must increase as well, but c cannot change (it is a constant, the speed of light). This means the only thing that can and does change is the mass increases.
Einstein united space and time into a single 'fabric' we call the space-time continuum. Keep in mind that he also united mass and energy. They aren't just related to each other, they are equivalent to each other! It is sort of like saying they are two forms of the same stuff. I like to think of ice and steam - there is no reason at all to think they are related just by looking at them, but with closer inspection they are both two forms of the same stuff, water.
In this video we will focus on the mass equation, and see what Einstein's energy equation is, where the notion of antimatter comes from, and where the idea of 'matter waves' comes from! These are some of the foundations of modern science, and we can derive them in just a few minutes. Check it out!!