Now that the basic combos in the deck have been adressed, I'm going to go over each card and why its important for the deck/the most optimal choice.
Crashing Footfalls - this card one of the two win conditions in the decks. Crashing Footfalls is insane when its able to resolve within the first fews turns of the game. Also note, this card can sometimes be suspended if you have a Gemstone Caverns with a luck counter on it.
Living End - the other win condition in the deck, requires more set up than Crashing Footfalls but the payoff is heftier and typically more game-ending
Electrodominance/as foretold - enablers for living end and crashing footfalls, see above.
Chancellor of the annex - one of the best cards in the deck. The pre game effect is extra helpful for us as were going to be on the draw. This is the best card in the deck to reanimate, but also the most dead draw. Do no keep more than one chancellor unless you also have an izzet charm in the opener.
Sphinx of foresight - fantastic to have in the opener to find oir combos and great to reanimate. It can be pitched to force of negation as well as being reasonably costed. There are definitely games where i hard cast this guy, either with lands or by having four counters on as foretold. Real solid beater, even turns on stubborn denial.
Waker of waves - both a fatty for our yard AND the means to get him there (instant speed and uncounterable btw). A 7/7 with an anti-anthem is rad, and its a pitch taget for foce of negation. I screamed with excitement when this silly uncommon was spoiled.
Gemstone caverns - really strange inclusion i agree, and often times you would think its just better to go first and in the times im second and have gemstone its no different than going first without it. However a play the deck really likes to make is gemstone on their first turn, simian into izzet charm, waker of waves, or electrodominance. Then on your first turn you play a land and cast finale of promise, or living end. Without this card its a lot more difficult to cast as foretold on turn 1, as you would need 2 simians otherwise. Stubborn denial on their first turn can be really funny too. The last thing to note about caverns is if you have multiple pre game effects and caverns is one of them, you can exile the other card AFTER its effect, to the caverns.
Simian spirit guide - the other source of fast mana. This card is integral to the explosive cheese this deck likes to pull off. On very rare ocasion you can play him as a 3 mana 2/2, which can later get reanimated.
Izzet charm - super versatile, instant speed, removal, counterspell, and pitch for living end. Can even be used to pitch to a force of negation. I dont think we can ask for much more in a card for this deck.
Force of negation - i hardly need to explain why this is included. We play very often on our opponents end steps or during combat, so force is amazing for protecting both the resolution of spells and creatures who have already secured a spot of the battlefield.
Stubborn denial - similar to force but good to protect on our turn, and to cheese people off playing on curve. All our win conditions active the ferocious effect of stubborn denial.
Finale of promise - i wish i could just run 6 electrodominance but alas, rules. Mostly just an alternative method to casting rhinos or living end. Casting crashing footfalls on endstep, and finale on your turn can be nasty. Creating 16 trampljng power quite easily with both this and electro dominance is crazy. Lastly theres a 4 mana play that can be made that just about instantly sets up our living end. Casting this spell where x=2 and targeting both living end and izzet charm is likely to load up a good living end.