Each time this perk is taken, it increases Unarmed damage by +5 points.
Iron Fist is a straight damage bonus during unarmed attacks, and does not increase Unarmed skill points.
In the world of hand-to-hand fighting, the player can choose to max 3 levels of Iron Fist for a 15-point unarmed damage bonus, which can be especially powerful early on when combined with power fists (26+15=41dmg). However, the player can also pursue the melee weapons route, which will save 3 perk slots, but be less powerful than unarmed combat until the level 12 Pyromaniac perk which turns the custom-built shortsword known as the Shishkebab into a powerhouse (60+3fire/5s).
However, Iron Fist can still pay off in late-game combat. With the use of a custom-built deathclaw gauntlet, the player can match the performance of the Shishkebab on many tough targets. Against deathclaws and power armored soldiers who average 45 DR or more, the Shishkebab does (33+2fire/5s) per strike. The armor piercing deathclaw gauntlet would do full damage (26+15=41dmg).
This higher base damage against armored opponents and comparable base damage against unarmored opponents is coupled with an incredible capacity to land critical hits due to the deathclaw gauntlet's x5 critical multiplier. It is quite easy to almost always land a critical hit with perks such as Ninja, Finesse, Survival Guru, etc.
Unarmed also pays off if the player takes the Paralyzing Palm perk, and the lowered critical hit rate from forgoing Ninja can be made up for if the player combines Grim Reaper's Sprint with Paralyzing Palm - allowing them to paralyze an opponent and kill another in one V.A.T.S. move, finishing with replenished AP.
Although only obtainable in Fallout 3, Ranger Stella from The Fort in Fallout: New Vegas has all three ranks of this perk.
“Channel your chi to unleash devastating fury! If you're the pugilistic sort and favor unarmed weaponry to inflict pain and suffering to an ever-more impressive degree, this is the perk for you! Let's not dwell on the slight shortfall of the difficulty in fighting multiple opponents at once; this focuses all your muscle on one hapless fall. Consult the Weapons chapter for the variety of punching weapons available.”— Fallout 4 Vault Dweller's Survival Guide description
Punching attacks now do double damage. Criticals in V.A.T.S. will paralyze your opponent.
Upon unlocking rank five, critical hits in V.A.T.S. while wearing power armor will no longer function; the Sole Survivor will simply stand idle while no animation is played or AP is consumed. [verified]
This perk works well with Martial Artist, which increases melee weapon speed and decreases weight, and Incisor, which causes melee weapons to ignore up to 75% of armor.
Behind the scenes
The following is based on unverified behind the scenes information and is speculative and may not be accurate.
The perk is may be a reference to the Marvel Comics character Iron Fist, whose chi-focusing abilities allow for powerful punches and attacks. This is further supported by the Fallout 4 version carrying the description, "Channel your chi to unleash devastating fury!"
End of information based on unverified behind the scenes information.