Perfection is attained, not when there is nothing more to add, but when there is nothing more to take away.
– Antoine de Saint Exupéry
The basic idea of Big Money is to maximize the value of each card in your deck. Where Big Money does that by adding only high value cards, the Chapel strategy is to trash your low-value cards.
Dominion distinguishes between discarded cards, which get shuffled back into your deck, and trashed cards, which go to the trash and are permanently discarded. A permanent discard sounds like a big cost in a deck-building game, but given attacks and curses, you can see why you would want to eliminate some cards. Several cards use the same mechanic to upgrade cards, turning a Curse (-1 VP) to an Estate (+1 VP) or a Copper ($1) to a Silver ($2).
A Chapel-focused strategy takes this to a greater extreme: all your starting cards are lousy cards, so let’s get better ones then throw away the original cards. The temporary setback is more than offset by having better turns the rest of the game. Remember, there is no cost to running out of cards and reshuffling your deck, so you can increase your chances of getting a good hand by adding strong cards (usually 1 per turn) or eliminating the weak ones (up to 4 every time you play Chapel). Once you have eliminated all the cards you do not want, Chapel is a dead card, but having one dead card is better than having ten.
Let’s take a quick example of how a Chapel strategy might start. The only possible splits in your initial two turns are 4&3 Coppers or 5&2 Coppers, and Chapel costs two, so if Chapel is one of your kingdom cards, you always have the opportunity to get a Chapel and a Silver in your first two hands. Your deck now has 12 cards: 7 Coppers, 1 Silver, 3 Estates, and 1 Chapel. The best possible next two hands are Silver + 3-4 Coppers (buy a Gold) and then trash whatever four you draw with the Chapel. In the best case scenario, your deck now has 9 cards: 6 Coppers, 1 Silver, 1 Gold, and 1 Chapel. You will want to trash those other Coppers as quickly as practicable, remembering that you might want to use them for a bigger purchase rather than trashing them this turn, and otherwise play Big Money plus whatever actions you like.
How has this opening helped? With your first 10 cards, your average hand value was $3.5. On average, you can buy a Silver per round. With your streamlined 9-card deck, your average hand value is $6.1. on average, you can buy a Gold per round. And this smaller deck both reduces randomization, because there are fewer possible hands, and even gains from randomization, because drawing a few high-value cards gives you a great turn while drawing a few low-value cards might let you streamline further by using Chapel again.
Let’s play that best case deck a few turns forward. You know your next two cards are Coppers, reshuffle, and the seven cards in your deck are known to be 4 Copper, 1 Silver, 1 Gold, and 1 Chapel. From here, everything is good. One great option is to draw two more Coppers and a Chapel; use Chapel to trash them all, and your deck now contains exactly five cards, so you are absolutely certain you will have $7 + Chapel next turn. Buy a Gold, and then buy either a Gold or a Province each turn for the rest of the (very short) game. At some point, you might be using Chapel to streamline Silver out of your deck.
This takes Big Money to its logical extreme and gives you very efficient turns. This also creates a degenerate strategy that takes much of the fun out of the game. If actions and interesting combinations are the fun in Dominion, Chapel streamlines the fun out. Some commenters have said they will not play deck-building games where trashing is this strong or present at all, the same way I will never play DotA2 or any MOBA where creep denial is a mechanic.
I said that making options more effective than Big Money was a major design goal for the expansions. If that was important because Silver is boring, you can imagine how much more important that is when burning your toys is a winning strategy.
Of course, the counters to Big Money work even better against a Chapel-streamlined Big Money. Thief and Pirate steal all your expensive cards. Chapel may counter Curses, but when your deck has only 10 cards, one Curse has a much bigger impact than tossing one into a 30-card deck. And a streamlined deck can bloat itself; you need to streamline Silver out of your deck when you have so many Provinces that you have trouble getting the $8 you need to buy another and finish the game. (Granted, good problem to have.)
Some expansions did create exciting combos more effective than Gold + Gold. But let’s be honest: it is hard to do much better than Gold + Gold. If Big Money taught you the importance of maximizing high value cards, Chapel should teach you the importance of minimizing low value cards.