Gomu Gomu no Culverin is one of the powerful techniques Monkey D. Luffy uses with his Gear Fourth in the manga and anime series One Piece. Culverin is named for a relatively simple firearm, ancestor to the musket and cannon. This technique continued to maintain its localized name of "Gum-Gum Culverin" in the VIZ manga and Funimation adaptations, giving consistency with the other rubber-based attacks of Luffy.
A Culverin is a Gear Fourth variant of Luffy's basic punch rush type of attacks. Fans speculate that it may be the next step of the Gomu Gomu no Hook, but official sources haven't clarified that point. Of course, just like all the other attacks Luffy made with his name, he would say "Gomu Gomu no" first, then the name of the technique.
In reality, the Gomu Gomu no Culverin is just an ordinary straight punch with the stretching abilities that Luffy has while being in Gear Fourth. That makes the move deadly because Luffy can then turn the direction of the punch in the mid-air to chase a moving target or steer out of the way when something's moving towards it. Such control over his rubber body further attested to the mastery that Luffy had over his power derived from the Devil Fruit, as well as further attested to the powerful state of Gear Fourth.
Some people view Culverin as one of Luffy's strongest techniques with Gear Fourth. Its efficiency derives not only from its power but also from its being versatile and unpredictable, providing its opponents with so many problems in dodging or countering it. This is difficult to dodge or counter even for enemies who are forewarned because the force of the punch changes its path.
Luffy has also demonstrated an enhanced version of this technique, called the Double Culverin. It is said to be one of the strongest techniques in Luffy's Gear Fourth. With Double Culverin, he likely brings forth both his arms to attack, doubling in power and making it a lot harder to avoid.
This is quite noteworthy because the Culverin is like most every other technique of Luffy's under Gear Fourth: there is no real convention of it in his base form or other Gear transformations. While other techniques, like the Gomu Gomu no Yari, boasting a Rhino Schneider version in Gear Fourth, have versions throughout the different Gears, the Culverin seems totally unique to Gear Fourth.
Luffy often names his attacks with Weapon/Animal jutsu terminology. Even the Culverin is a reference to a very old kind of firearm so it fits this trend, but it also refers to the explosive power of the technique.
In this sense, what the Culverin really represents is that it's a huge step forward to Luffy's general way of fighting. It takes all the power improvements and added flexibility of Gear Fourth and applies them with an accuracy and consideration Luffy rarely shows in his own natural state. In actuality, it isn't just Luffy's increased power in Gear Fourth; it shows ingrown tactical acumen and plasticity of powers in really imaginative ways.
The Gomu Gomu no Culverin, on the other hand, has really been shown in some top fights in the series as an ability that is effective against top-class enemies because it is capable of redirecting direction in movement while associating an attack and surprising many adversaries. Many are the times it turns the tide at crucial moments.