Bisq is decentralized which means that there is no central component that, if removed, would cause Bisq to fail. For instance, the exchange data such as offers to buy or sell BTC is not stored on any central server. You do not need to go to a central website to trade. Instead, you download and install the Bisq application on your computer. The Bisq app is free/open-source software (FOSS) which is maintained and improved by a network of contributors. By running the software, your computer becomes part of the Bisq network.
There are many different payment methods that you can use on Bisq. For instance, if you are using MoneyGram to receive USD in exchange for BTC, you need to add information about your MoneyGram account so that your trading partner can send you USD. Bisq does not automatically send the USD from your trading partner to you, it just gives them the information they need to send USD to your MoneyGram account. Since your data is stored locally on your computer, the rest of the network doesn't know the details about your MoneyGram account.
The app contains an internal BTC wallet. Upon starting the app, you are encouraged to write down your seed phrase and backup your wallet data. You are responsible for your own funds since the rest of the Bisq network has no access to them. Anyone can make an offer to buy or sell BTC, and you are free to take that offer or not. When you take someone's offer, under the hood your Bisq software communicates with that of your trading partner. Both of you need to make a security deposit as insurance against potential fraud by either of you. That deposit is locked in 2-of-3 multisig which includes you, your trading partner and an anonymous Bisq arbitrator, and can only be unlocked if two out of three people agree. In the event of a dispute, an arbitrator investigates the trade and determines the right course of action.
You can learn more about the Bisq software on the Bisq website.