To get coins, people typically use powerful software installed on their computers. This software helps process transactions on the coin's network by solving complex math problems. By powering these transactions, miners are rewarded with coins. This is what we call mining.
Browser mining is a relatively new way to mine for coins. It uses special scripts that let your browser (Chrome, Firefox, etc.) process these transactions. Every time your browser helps process a transaction, you get rewarded for it. All you have to do is leave TabMine open and running - that's it!