How do we measure the age of the universe? As mentioned in wiki/Age_of_the_universe,


  The current measurement of the age of the universe is around 13.8 billion years (as of 2015) – 13.799±0.021 billion years


When my friend who is not from science background asks me how do we measure the age of the universe? How should I explain to him?
Once we look far enough away to get past "local effects" we see everything moving apart, spreading out in all directions, like a set of dots on a balloon being inflated, or like currants in a loaf of bread rising in the oven.

We can use the laws of physics to follow those movements back in time to work out how far apart all the galaxies were at various dates in the past. If we do this we find that 13.8 billion years ago they were all in the same place (there are a lot of subtle details to get right in this calculation, but a lot of people have worked on it over a long time). That much matter and energy packed into that small a space warps both space and time so that it is not really possible to talk about time "before" that event. Hence that is taken as the origin of the universe.