We are using IPFS. What is that?

IPFS is an upgrade to HTTP, which is the protocol your web browser used to bring you here. When you type a website into your browser, it "asks" another computer – usually, but not always, your internet provider – how to get to the site and then loads the page.
This can be problematic, as it centralizes accessing information to a handful of companies.
IPFS removes the need for that middleman, as the request is sent to the entire network. This network is made of other users like you. So when you "ask" for a page/object, the network points you to the correct place; no centrality is needed.
What makes IPFS incredibly compelling for Anytype is how it provides an address to every unique object. For example, if you're looking for an image, you won't need to request an entire website – with all the nonsense found these days – just to view an image. Instead, you can request that object, and the network will point you to it. This enables Anytype users to build a personal web of knowledge, with the ability to share and connect with others on their terms.
When we talk about blockchains, we refer to something like Bitcoin or Ethereum Classic. In these cases, a blockchain is a massive file that contains a record of every action on the network. Every user of the web keeps a copy of this record. This record cannot be changed. In IPFS, each network node stores only content it is interested in, plus some indexing information that helps figure out which node is storing what, so you don't need to copy the whole internet.