When the DM believes the player has played well and worthy or a reward the DM will grant a character "Inspiration". A character can only have one "Inspiration". The character can use this to give their character an advantage roll on an attack, saving throw, or skill check. Of course the character should declare they are using their inspiration before making the d20 roll.
PH page 125.
I think I may introduce this mechanic in my 3.5 campaigns.