I will try to explain what it means in terms of exclusive control of spending. Most of the centralized exchanges like Binance are custodial. Why? Since the exchange itself can control your assets via withdrawing and you have to use an intermediary to spend your assets. You have to trust the exchange on this: “they will be honest and not deceive you”. On the other hand, some DEXs like Binance DEX, pDEX are non-custodial. Why? Nobody but you can access the private key of your wallet. So nobody but you can spend your assets and you don’t need any intermediary to spend your assets. So you do not have to trust anyone, i.e. “trustless”.
Incognito uses bridge wallets while you move your crypto assets among internetworks. It uses a smart contract for Ethereum bridge. A smart contract can be used to support "trustless"ness if it is coded accordingly. The team claims that Ethereum smart contract of Incognito is trustless by claiming that the Ethereum-Incognito bridge is trustless. So when you deposit your some ETH to the wallet given by the app, it is required that a third party without any pETH must not be able to withdraw any ETH. To illustrate, assume that the bridge wallet is empty and someone deposits to 5 ETH into it. Then, she doesn’t perform any trade and she wants to withdraw all of them. However, they couldn’t do this since the bridge has less than 5 ETH. Why? Since someone has withdraw right through the code of the smart contract and spent some ETH in the bridge. To sum up, Incognito team claims that this cannot be done by even itself. Is it true? To my audit, it is not completely true (not a bug, intentional) but as I remember (or hope, not sure ), they will make it the completely trustless.