STAB stands for Same Type Attack Bonus.
So if I had a Magby and it used Ember, it would get STAB seeing as both are Fire type.
Ember's power is 40 but with STAB adds on 50%, so
40 x 1.5 = 60 so Embers power becomes 60. Duel types like Crobat will get STAB on two types - in Crobat's case Poison and Flying moves will get the 50% bonus.
More information on the type chart page.