MicroCash differs from Bitcoin (and nearly every other cryptocurrency) in that it has a distributed ledger of accounts. It is much like a normal bank account in that there is a balance but instead of a name “John Smith” there is a random address which looks something like “SXTNFWJWXTPBLI4GM” . To prove you own a MicroCash account you must prove so by signing a transaction with your private key that only you should ever know.
In Bitcoin there is a list of inputs and outputs in every transaction. For every input in a transaction you must sign it to prove you own those funds. In the Bitcoin system it is like proving you own every transaction ever put into your bank account instead of merely proving you own that bank account.
Consider if every time you withdrew from your bank account you had to prove how every dollar got in there in the first place, it would be tiring right? Well it’s also tiring for the Bitcoin nodes themselves to prove it which is one reason why Bitcoin transactions are slower than they could be.
MicroCash instead is much like a distributed bank in that anyone can run and verify the bank, unlike traditional banks which aren’t transparent and can be controlled by people nothing in MicroCash can be controlled by people who don’t own a particular account.
So it’s much like how a bank should be in theory, an irreversible place for you to store your savings that the government, or corporations cannot remove from you.It is much simpler to process for the nodes as they only have to verify you own a single account, not prove how everything ever got in there.
You might ask why Bitcoin never adopted this method in the first place as it is a lot more efficient. I’m not sure if Satoshi ever mentioned it himself but I think it was believed that it would be more privacy orientated. But it isn’t really, in some ways it leaks specific knowledge such as when particular coins get spent. For instance imagine a scenario where an account has 5 transactions of 100 coins each put into it. One of those transactions may have originated from a sensitive origin which we will mark with an asterix *
   [*100*] 
In Bitcoin or MicroCash the user would have a balance of 500 but the difference is how it is stored. Bitcoin stores it like above, 5 transactions (which can be 100000 bytes each) whereas MicroCash simply stores it like this  which only takes up 8 bytes.
Over time the knowledge of how that account ever got 500 in it would be lost in MicroCash as that information is not important to it or the nodes. In Bitcoin the “dirty transaction” marked with an asterix has to be spent exactly like it is and you would know exactly when and how. This is why Bitcoin hackers immediately start to divide and attempt to obfuscate anything they have stolen, because there is zero privacy really afforded to them without creating thousands of useless transactions which bloat the blockchain and slow down nodes.
You may argue that by putting that [*100*] into a MicroCash account you have tainted the entire account, the entire 500 is now tainted like this [*500*]. But this also means every single account in MicroCash could also easily be tainted by people distributing their funds in donations and gifts until you would never know what is tainted and what isn’t. If I spend  of that [*500*] is it using one of the first 4 transactions or the dirty one? No one knows. If everything in MicroCash is “tainted” then worrying about taint in a single account is nearly pointless. Services which wash coins have a very easy job compared to Bitcoin.