Monero's privacy comes from two mechanisms, and neither one requires you to understand the mathematics to understand what it does for a deposit. Here is what each one hides and why the combination is what makes Monero the privacy default on a market like Awazon.
Ring signatures
A ring signature mixes your transaction with a group of other plausible transactions, so that an observer sees a ring of possible senders and cannot tell which one actually signed. Your output is in the ring, but so are several others, and the protocol is built so that no member of the ring can be distinguished from the rest. The effect is that a payment from you looks like a payment from any of the others in the ring. It does not hide the fact that a payment happened. It hides who sent it.
Stealth addresses
A stealth address is a one time address derived for a specific payment, so that the destination you see on the chain is not your usual address. Each payment to you lands at a fresh address that only you can derive the key for, which means a watcher cannot link two payments to the same recipient by matching addresses. The effect is that a payment to you does not advertise your identity the way a payment to a known address would. It does not hide the fact that a payment was received. It hides who received it.
What the combination means for a deposit
Together, the two mechanisms hide the sender, the receiver and the amount, which is the full set of things a Bitcoin deposit leaves on a public ledger. A Monero deposit to a market address leaves a transaction that is hard to attribute to you, to the market, or to a specific value. The honest limit is that Monero reduces the trail, it does not erase it. A determined analyst with the right tools and the right starting point can still narrow things down, and the network effects of using a privacy coin are not invisible. But for the ordinary case, a buyer who does not want a deposit sitting on a readable chain, Monero is the coin that gives the strongest practical protection without any extra work on your part.