In a peer-to-peer network (P2P), every participant plays the same role; they are all peers. Each peer is both a client - requesting data, and a server - providing data. 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 connect directly to the server. If this computer happens to have a problem, the website won’t work. With a P2P networkn the other hand, if one machine becomes unavailable the remaining machines continue to provide services.
In a P2P network, you are usually connected to several peers and if one goes offline, everything still works as usual. This makes blockchain networks very robust.