Falcon Punch refers to Captain Falcon's neutral B attack. It is one of SSBM's most powerful moves, with the highest knockback of any of Falcon's attacks (including charged smashes). This move is one of the few attacks in the game that is more powerful than the Home-run Bat at high damages (combined with the fact that Captain Falcon's home run attack flies upwards rather than sideways), and thus players use it in Captain Falcon's world record Home-run Contest strategies. Falcon Punch is also very slow, with a start-up time of 52 frames. As with all neutral B attacks, this move can be redirected by tapping the analog stick in a direction, returning it to neutral, and pressing B quickly.
In Brawl, Captain Falcon can turn around during the start-up of the punch. It does slightly more damage.
Combos into Falcon Punch
Despite the slowness of Falcon Punch, there are a few situations where a launcher (namely, down aerial) can combo into Falcon Punch.
Tapion Punch Combo
Named after Tapion, this two-hit combo leads into Falcon Punch after an l-canceled down aerial. It works on Fox as low as 75% damage, Falco as low as 78%, and C. Falcon as low as 80%. It can be avoided with Directional Influence.
G-Regulate's Falcon Punch Combo
Named after G-Regulate, this combo works similarly to the Tapion Punch Combo, but uses a platform. Captain Falcon must l-cancel a down aerial onto a platform so that it hits an enemy below him. Against some characters at some damages (notably Marth at 65%), Falcon can combo his down aerial into Falcon Punch. It can be avoided with Directional Influence.
Popular Culture
The Falcon Punch is a joke on the website 4Chan and other sites. There, the move is the ultimate embodiment of manliness, expelled from the fist. Additionally, when an abortion is mentioned, the Falcon Punch is referenced as the best abortion method.
References
SuperDoodleMan's frame data SSKeeto's Home-run Contest guide