On a high level, I2P is an overlay internet on top of the regular web. Everyone has a router address that acts like a regular IP address, except that this one is purely inside the I2P software. So unlike IP addresses that go over your ISP to connect to the internet, on the I2P network your router can connect to other routers directly without the concept of ISP.

Your traffic makes multiple unidirectional hops over nodes in the network before it accesses the site/peer you want to connect with. Connection from your peer back to you goes back over another set of unidirectional nodes (unlike TOR where contacting and receiving uses the same set of nodes). The connection between the nodes uses the latest encryption methods of course.

For more details you would have to ask someone else.