From my understanding, i2p is an anonymity focused way to access the Internet. It cant access normal websites, but it can access I2P websites. The main difference between i2p and tor routing is that i2p uses what's called "garlic routing" and tor uses "onion routing". Without getting into specifics, unlike Tor, on i2p in order to join the network you also have to let other people's traffic go through your computer. This is called being a relay. I2p initially started as a way to obfuscate your IP address to access IRC channels, but has been expanded to be its own dark web.

i2pd is just the program that would allow you to connect to the i2p network. Usually when a program has the letter d at the end, it's what's called a daemon, which is just a program that sits in the background waiting for you to ask it to handle something. In this case i2pd is waiting to handle your i2p traffic.