Things just seem to go your way, more often than not.
You have a pool of Luck Points equal to half your Proficiency Bonus. Whenever you make an Attack Roll, Ability Check or Saving Throw, after seeing the result of the roll but before learning of it's effect, you can use your reaction and spend a Luck Point to add a bonus to the Roll's result equal to your Proficiency Bonus. For example, at level 16 you have a Proficiency Bonus of +5. Halving this gives you a pool of 2 Luck Points to spend (as you always round down unless otherwise stated). When spending a point in this example, you would add +5 to the Roll's result.
You can also spend a Luck Point when a creature makes an Attack against you, to increase your AC by half your Proficiency Bonus for that attack. In the same fashion as the first effect, you may only do this after the Attack has been rolled but before you learn of it's effect.
You regain all of your spent Luck Points when you finish a Long Rest.
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