From Sonic Retro
At key points in Tag Team stages, Sonic and the Avatar will focus their power into their hands and then high-five each other. Then, the player is prompted to repeatedly press the (PS4)/ (XB1)/ (Switch) button within a few seconds to power up the boost. If performed correctly, Sonic and the Avatar will boost away like when performing the Boost, but at far greater speeds, while a short version of Fist Bump replaces the background music. In some cases, Fist Bump replaces the background music in its entirety. The Double Boost ends when the Boost Gauge runs out, but it can be refilled by destroying enemies and collecting Rings. If not done correctly, Sonic and the Avatar will stumble for a second before the aforementioned Boost is performed along with the vocals being cut off.
The Double Boost is required for the numerous instances where it is used, such as escaping Null Space and Final Judgement, and to land the coup de grace against Metal Sonic and the final battle against Infinite.