In a Peer-to-Peer network, every participant is connected to everybody else. When you compare it to a regular website, this makes it a lot more robust. A special computer on the internet stores most websites. This special computer is commonly known as a server. If you want to access the website, you will connect to the server. If this computer happens to have a problem, the website won’t work.
In a Peer-to-Peer network, your connection may get lost as well, because a peer goes offline. But you can connect to another peer on the network and everything works as usual again. This makes blockchains and cryptocurrencies very robust.