Input Buffering, sometimes just Buffering, is a term for a gameplay concept that can be used in DmC: Devil May Cry, which allows the player to create more seamless combinations of attacks.
Input Buffering shares its history with Capcom's other greatest genre - Fighting games. In fighters, input buffering is an essential part of high level play, especially when performing special attacks and even Supers require lengthy input commands. That same mentality can be brought over to DmC to increase the flow of combat in the player's favor.
Buffering is a mechanic in place that allows the player to mask the input of one attack while a preceding attack's animation is playing out. This is most prevalent in regular gameplay where you press an attack key before the previous attack is done to continue a combination attack. However, higher level play requires a bit more than just repeatedly mashing a key.
A great example of such a thing is performing a regular Hacker combo with Rebellion, but during the animation of the last swing performing the inputs for Stinger so Dante immediately slides toward the enemy after finishing Hacker. This can also be done with "Hold" moves, or moves that require you to hold in the attack key to charge up, like Drive, or Raze. Performing regular combos and leading them into Hold moves can be beneficial to shortening the time required to execute the Hold.
When learning to use Buffering to your advantage, the best thing to do is take note of each attack's "Buffering Window," which is how many frames into an attack's animation it will register another input, along with how far through the attack's animation it must go before the input is turned into action. Some abilities have smaller windows, requiring the player to place inputs as closeer to the end of the move as possible, like Rebellion attacks, while some have quite large windows, like Inverse Rainstorm, which will register an input almost from the start of the attack's animations, but it won't perform the registered move until Dante finishes his ascension.
Buffering can also require knowledge of what the move can and can't be canceled with. For instance, Inverse Rainstorm, which it's large buffering window, will register an input from Rebellion, but won't perform the melee attack until Inverse Rainstorm is finished. However, If you use a firearm's normal attack, like Ebony and Ivory's Shoot, Inverse Rainstorm will be immediately canceled into the regular shots. Using cancels and buffering together as part of the player's repertoire can result in better combos, and overall more stylish combat.