On an attack that hits, you may add one of your hit die to the damage. In return, you also take that damage. When making athletics or acrobatics checks, you can add a hit die to your roll AFTER you know your total but BEFORE the DM tells you the outcome. You also take that damage. You gain a +1 to your constitution score. If you have d10 hit dice, and you hit a creature, you may roll a d10 to add to damage. If you roll a six, the creature takes six more points of damage. You also take six points of damage. It is always the same type of damage as the attack, and resistances still apply, so if you have fire resistance and added that die to a firebolt, you would only take three points of damage.
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