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Grayflame requires that you have the ability Channel Energy or something equivalent to it like the Lay on Hands ability of a Paladin.
A character with the Channel Energy has some associated about of positive or negative energy damage it deals based upon their character level and their alignment or that of their deity. A 1st level Cleric of lawful good alignment for example has Channel Positive Energy 1d6.
If she were wielding a +1 Grayflame Mace, she could spend her swift action and mark off one use of her Channel Energy ability to have the mace gain an aditional +1 to hit and damage as well as an extra 1d6 of damage for 1 round. The flames on the mace would be silvery gray, the mace would bypass good and/or silver damage reduction and the bonus damage it deals wouldn't affect other good aligned creatures.
This weapon responds to channeled positive and negative energy.
When the wielder spends a swift action to channel energy through the weapon, it ignites with a strange gray flame that sheds light as a torch, increases the weapon's enhancement bonus by +1, and deals +1d6 damage (as the divine power from flame strike) to creatures struck by the weapon. This flame lasts for 1 round for every d6 of damage or healing the channeling normally provides. When charged with positive energy, the flame is a silvery gray, good creatures are immune to the weapon's extra damage, and the weapon counts as a good and silver weapon for the purpose of bypassing damage reduction. When charged with negative energy, the flame is an ashen gray, evil creatures are immune to the weapon's extra damage, and the weapon counts as an evil and cold iron weapon for the purpose of bypassing damage reduction. This special ability can only be placed on melee weapons.
1) The grayflame weapon ability requires the user to have the channel energy ability. The user can usually only channel positive OR negative energy not both (see a clerics channel energy ability).
2) The +1 enhancement bonus gives +1 to attack and damage. Also the whole point of the grayflame is that it does an extra 1d6 divine damage per successful attack. However evil creatures are immune to it if the weapon was charged with negative energy and good creatures are immune to it if the weapon was charged with positive energy.
3) The number of rounds the flame stays on is equal to the number of dice your channel energy ability can currently do. Example: A level 3 cleric can do a 2d6 channel. So their grayflame weapon will last 2 rounds.
4) Some creatures have Damage Reduction which strangely enough reduced damage from weapons done against it. This Damage Reduction (called DR for short) can be bypassed if the weapon attacking the creature is made of a certain material. It's not that it does extra damage, it's that it ignores DR.