The Big One is the final upgrade of the path 1 for the Mortar Tower. It costs $8500 (Easy), $10000 (Medium), $10800 (Hard), $12000 (Impoppable). It makes devastatingly large explosions, each popping through 5 layers of Bloon. This upgrade is unlocked at Rank 37.
In the Mobile version, it is not nerfed (meaning that it can still pop 5 layers). It appears that the description has an error in it. The description says "Devastating explosions each pop 3 layers of bloon." but in the update, it corrected it by replacing it to 5 layers.
These are useful for making the game lag less because of how large the explosions are, with the huge range along with the fact that they take out more bloons instantly.
If the player adjusts the aim for a Mortar Tower with The Big One on the center of Mt. Magma, or the center of 3 Times Around's circle, it will cover the entire circular center.
This is the only upgrade to increase the popping power of Mortars. Every other Mortar upgrade has a popping power of 40, while The Big One has a popping power of 100 (in addition to popping 5 layers, meaning the Big One can pop up to 3,100 bloons in a single shot (if it hits 100 Ceramics with 1 HP left).
The monkey next to The Big One seems to wear the same clothes as a Glue HoseGlue Gunner, but the cloth is protecting the monkey from radioactive mortar shells and not from glue.
According to the upgrade picture, The Big One cannot safely be touched by the monkeys (even with gloves) without the help of tongs to insert the mortar. However the monkey is not using them in-game, so the upgrade picture could be purely for emphasis to show how dangerous The Big One is.