The subject of conversation on crypto-twitter recently has been merkle trees.

This uses blockchain explorer data snapshots to verify cryptocurrency wallet balances on centralized exchanges, and show transaction history of these wallets, which verifies ethical practices and provides some protection to the cryptocurrency investor and depositor of funds on these exchanges.

Proof of Reserves .

A very brief explanation is that, it is a way of verifying that centralized exchanges actually have all the money investors deposited into them (the exchange) in their wallets, and by following the money trail, verify that exchanges are not using investor funds improperly. For example for risky investments and personal purchases.

How does it work?

in brief, the idea starts off with the blockchain explorer, a ledger, which records all transactions on a blockchain. And it allows you to look at a specific wallet address, and verify their balances. For example, if the exchange says they have received 2 million Bitcoin deposits, their wallet address on the Bitcoin blockchain explorer should show they have 2 billion Bitcoin. If they don't have 2 million Bitcoin, the blockchain explorer shows where it went.
Taken a step further, you can use the blockchain explorer to look at the data of many transactions, from many investors, sending hundreds of different cryoptocurrencies, over several days, weeks, months, and years.

What is a Merkle Tree?

A Merkle Tree is a cryptographic tool that enables the consolidation of large amounts of data into a single hash. This single hash, called a Merkle Root, acts as a cryptographic seal that “summarizes” all the inputted data. Additionally, Merkle Trees give users the ability verify specific contents were included within a particular set of “sealed” data. Exchanges or blockchain explorer analysts can use these properties of Merkle Trees to perform Proof of Reserves assessments. source

In close to plain English,

... a Merkle Tree is kind of an immutable and verifiable data snapshot. It stores the transaction data in a way that knowledgeable users can access the and verify the data. Additionally, it verifies the data in a large content pool. This helps the exchange users to trust that their crypto holding is safe using public blockchain information to verify it's presence.
source

In very plain English, it means you are utilizing the blockchain explorer to first check the wallets balances of centralized exchanges to verify they have all the cryptocurrency in their exchange wallets that they are suppose to have in their wallets, based on deposits. And second it's a way to analyze blockchain wallet transaction records to prove exchanges aren't taking money out of wallets that hold investor funds and investing them in other exchanges or project wallets improperly.
It's a very accurate way of examining wallet balances and tracking cryptocurrency movements.
So in theory because it's a built-in way to gather large amounts of data, it is reliable, because it hasn't been altered by the collection process. So it's considered very reliable. So it's used to Prove Reserves and verify ethical storage habits of exchanges regarding investors funds.
In cryptographic terms this allows a blockchain examiner to verify both cryptocurrency balances and transactions in a real time, from immutable (unalterable) sources, due to crypotographic protection, as long as the blockchain hasn't been rolled back and altered, which is also a recorded event.
This is Proof of Reserves via Merkle Tree.
It's complicated, but it's an attempt to use the transparency of the blockchain explorer, along with the integrity of the cryptographically blockchain explorer, to verify the presence of reserves in exchange wallets, along with their movements, thus indirectly prove ethical storage habits by centralized exchanges.

Another reason to use a Merkle Tree for Proving Reserves? Privacy.

Creating a Merkle Tree from the complete list of user account balances enables an exchange to offer data, in a privacy preserving method, which verifies that the cryptocurrency funds are in the exchange wallet. Through this process, the exchange can publish the Merkle Root Hash, which is the data reflecting transactions. And preserve customer privacy. source

Apology to author: Please excuse my paraphrasing and substitutions of plain English words, to explain, what you so elegantly explained in cryptocurrency language.

In English, it's technically easy, or easy to do for cryptographic blockchain explorer analysts. It's a native feature, or something built into blockchain explorers. A Merkle tree is a convenient unit of account, which is built into many cryptocurrency blockchains, and Merkle Tree data can be verified as true. So open source software was been created to obtain data from wallets and in theory it can be trusted.

Why do we need these things?

The main reason is that cryptocurrency was created was to allow you to completely control your cryptocurrency.
And it did so literally with Cryptographic Security so strong and unbreakable that the US Government fought legal battles to keep this cryptographic security to itself.
It is the very best security in the world currently, and is not hackable by our best computers in less then 100 years.
However using this secure system requires knowledge and attention to detail.
In the absence of this knowlege and attention to detail all an investors cryptocurrency can be lost if you lose your passwords, because without them, you can't break into your cryptocurrency wallet.
So you need backups of your password.
Most investors don't utilize the full security of cryptocurrency, and instead choose less secure ways to invest and own cryptocurrency, by keeping it on a centralized exchange.
Which shifts the responsibility for securing the cryptocurrency from the investor, to the centralized exchanges.
This system is easy, and it works. But depends on the honesty and integrity of the exchange or project you are investing in... and recently several exchanges have shown themselves to be dishonest and to lack integrity.
Now in the traditional financial world, honesty and integrity are normally guaranteed by both the importance of reputation, and the threat of regulation and enforcement actions. The later periodically result in inspections, examinations, fines, and jail time for the dishonest.
But due to the lack of clear regulations in the US, and a history of regulation by enforcement actions..defined by some as you don't know what the law is, until your break the law. (An opinion)
This has driven many exchanges out of the US like Binance, and deprives their investors of the usual type of protections they enjoy in stock, bond, and other traditional financial markets; from US finance laws and regulations. (An opinion)
Proof of Reserves tries to introduce an element of verification into this trust gap between exchanges and investors, in the absence of financial rules and regulations, along with government regulator oversite.

The problem with merkle trees

The problem I see is that this requires knowlege and understanding, and in my opinion, it is the lack of these two things, which got retail and institutional crypto investors into this mess to begin with: the mess is having their funds misused and stolen from centralized exchanges.
And now we are being offered a proposed solution, which requires significant knowledge and understanding, as in Merkle Trees, which are fairly complex, and the typical investor can't use them, so they just have to trust the exchange anyway.
Quite frankly, to me, by comparison, understanding how to self custody your own cryptocurrency may be simpler. I am not saying simple, but simpler.
This is of course not financial advice, just information, and metaphorically speaking Food for Thought.