Welcome to the combo explanation.
Section 1: First, lets understand the Ripple effect from Thrumming Stone. This card has ripple 4 and this needs to be in play for the combo to go off. What is Ripple? Great question the answer is below.
1a. Ripple is a triggered ability that When you cast a spell, you may reveal the top 4 cards of your library, or, if there are fewer than 4 cards in your library, you may reveal all the cards in your library. If you reveal cards from your library this way, you may cast any of those cards with the same name as this spell without paying their mana costs, then put all revealed cards not cast this way on the bottom of your library in any order.
Section 2: Now lets look at the interaction when you cast your first Shadowborn Apostle. When the Ripple 4 trigger resolves and you reveal the top 4 cards of your library. For every Shadowborn Apostle revealed this way you can cast it for free and trigger the Ripple 4 again for each additional shadownborn you cast this way. So, you pretty much get to cast every Shadowborn in your library. Unless, you hit 4 non-shadow born Apostles on your first Ripple (example you reveal 4 Swamps). Sections a-e breaks the combo down even further. If you get how it works please feel free to skip to Section 3
2a. We will start from the beginning. You already cast your first Shadowborn Apostle. Once it resolves the Ripple 4 will trigger from Thrumming Stone and you reveal the top four cards of your library. Lets say you revealed 2 Swamps and 2 Shadowborn Apostles
2b. The Swamps go to the bottom of your library.
2c. Now it’s fun time! You revealed 2 Shadowborn Apostles and they indeed share the same name as Shadowborn Apostle! The best part of Ripple is you now get to cast them for free. Resolve each one at a time and cast your first Shadownborn that was revealed in the First Ripple 4 trigger. Now you get to Ripple 4 again!
2d. Reveal the top 4 cards of your library again and cast any card that shares the name Shadowborn Apostle. Lets say on your first one you reveal only 4 swamps. This is not an issue because on your first ripple 4, you revealed 2 Shadownborn Apostles and that means you get to Ripple 4 again. However if for some unknown reason you get 8 swamps in a row on the two ripple 4s you have the worst luck in the world and try again next turn.
2e. You should now get to cast every single Shadowborn Apostle in your deck (as long as you don't wiff) and you should get all of your Shadowborn Apostles out on the battlefield this way.
Recap: You cast your first Shadoborn and Rippled 4 and revealed 2 Swamps and 2 Shadowborns. You cast the first Shadowborn that was revealed from the first Ripple and Rippled 4 again and you got 4 swamps then you resolve the second Shadowborn from your first Ripple 4 again revealing 4 more Shadowborns and then you get to start the process all over with the 4 newly revealed Shadowborn.
Section 3: Now Cast Tendrils of Agony right after you cast all your Shadowborn Apostle and kill as many opponents as possible. Even if someone counters that spell it still triggers for every other Shadowborn you cast. So, if you cast 48 Shadowborns they will have to counter 48 spells!