Yggdrasil (200::/7) is a friend-to-friend meshnet with end-to-end encryption that carries mostly IPv6 traffic.
Maybe read the whitepaper for a description of how it works.
Think global IPsec - but it actually works.
It is kindof like the ordinary internets, except that it is "secure" by default. Secure, as in that all packets are encrypted end-to-end and authenticated. MITM-attacks are not possible: The nodes IPv6-addresses are the hashes of their public keys, so it is essentially impossible to impersonate any other node (not physically impossible, but quite impossible, depending on your trust in the science of modern cryptography). Routing is done using a novel DHT mechanism based on oldskool Kademlia. This also means that Yggdrasil does not rely on central authorities for addressing or routing; bureaucrats have no say, it is decentralized. There is no politics involved in routing decisions, unlike the intertubes.
Yggdrasil have a simple built in firewall that inspects packets before the operating systems firewall does it. It can be configured to only allow packets that belong to sessions that only you have initiated, or to only allow directly peered nodes to initate communication with you. It is useful for setting up clients and server infrastructure, respectively. See "SessionFirewall" in the docs. (The IPsec-like features of Yggdrasil are perhaps useful by themselves, even if you do not want to participate in any global network.)
Yggdrasil does not (yet?) provide hidden services, like Tor onions. You can however borrow this feature from Tor/I2P by routing over them - if you only peer via Tor/I2P (use the built-in SOCKS5 proxy client) then you are effectively anonymous (technically pseudonymous, since the node IPv6 address remains until you replace the nodes cipher keys). Routing over Tor/I2P is as slow as you would expect, and the tunnels eventually temporarily collapse.
The network only have maybe 300 nodes attached to it now: It is what you bring with you = it is what you build out of it. The Yggdrasil community is perhaps mostly made up of misfit sysop hackers and twisted turbonerds.
An entry-point is provided by cryptoanarchy.org: Peer details.
If you want good anchors in Yggdrasil, you need to find more peers and build tunnels of your own. It is probably most healthy when its links are friend-to-friend.
Other known entry-points: Git repo.
This map of The Yggdrasil (alternative link (inside)) does not show all the pathways - it only shows the branches used for navigating the net in O(log(n))-time. (?)
A list of public services. Some of them are only accessible from the inside.