How to explain ETH to undergraduate students?
It seems that you are aiming to convey the significance of disproving ETH? If you're looking to leave some impression, it's always better to show rather than tell.

I think your students need to see some examples of practical areas and difficult problems that efficiently reduce to SAT. If you can demonstrate to them that SAT is a "funnel" of sorts for many other kinds of problems, your students can piece together for themselves why solving SAT in sub-exponential time would be game-changing. 

Some example problems could include task scheduling, the traveling salesman problem (and by extension, pretty much any sort of path-finding problem), register-allocation in code compilation, general propositional logic inference, etc. You can also discuss industries that use SAT-solving already, like circuit design and e-commerce.

This would take a fair bit of work, but you could even demo using a SAT-Solver; Sudoku is a popular and relatively easy example problem, and it never fails to amaze me how quickly it solves even the hardest of puzzles. If you need one, CryptoMiniSat is a great off-the-shelf SAT-Solver https://github.com/msoos/cryptominisat/releases.