Mastering a game is beating it. Here's a link to the faq explaining it-
Retro Uprising - FAQ
It's number 4 & 5 in the game rules section.
The gist of it is you have to submit a screenshot showing the game is beaten. You submit a screenshot for mastery or high score by pushing F12 on the correct screen. Most games can be mastered but for various reasons not every game is eligible.
Welcome to RU, let us know if you have any more questions.