We're... not entirely sure.
WHat's most likely to happen, though, is that Nirn will... dissolve, for lack of a better term. From my understanding, the Towers are like physical pins, keeping the fabric of Mundus together. Once the last tower goes, Mundus would unravel, and return to a pre-creation state.
That is the ultimate goal of the Thalmor. And they're going after multiple targets; Talos to weaken the nine and cause Mundus to unravel, the towers to cause Mundus to unravel, and probably another, seperate thing that would end up causing Mundus to Unravel.