IPFS stands for the InterPlanetary File System. IPFS is a bold attempt at evolving the Internet's infrastructure.
# IPFS Paths
IPFS paths begin with a multihash and can be followed by an arbitrarily long path. Each path component is looked up in each IPFS nodes link-list until the final blob is retreived.
Animated gif showing the resolving of an IPFS path - github 
/ipfs/<hash-of-foo>/bar/baz /ipfs/<hash-of-bar>/baz /ipfs/<hash-of-baz>
IPNS stands for the The Inter-Planetary Naming System. ipns is a way to add a small amount of mutability to the permanent immutability that is ipfs. It allows you to store a reference to an ipfs hash under the namespace of your peerID ( hash of your public key ).
YOUTUBE HUVmypx9HGI Stanford Seminar - Juan Benet of Protocol Labs
Quote by Juan Benet
Here's how Juan Benet (@juanbenet) describes it:
IPFS is a global, versioned, peer-to-peer file system. It combines good ideas from Git, BitTorrent, Kademlia, and SFS. You can think of it like a single BitTorrent swarm, exchanging Git objects, making up the web. IPFS provides an interface much simpler than HTTP, but has permanence built in. You can also use it to mount the world at /ipfs.
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IPFS uses a global local object repository, added to ~/.ipfs. See the full instructions over at ipfs.io 
Here are some introductory videos, or just head over to GitHub and give it a try - GitHub .
YOUTUBE 8CMxDNuuAiQ
An overview and demo of the go-ipfs alpha - GitHub
Below is a Talks at Sourcegraph @juanbenet gave about his project, "IPFS: The Permanent Web" (slides and video):
YOUTUBE Fa4pckodM9g Juan Benet discusses his project, IPFS, which is a global, versioned, peer-to-peer file system that combines ideas from Git, BitTorrent, Kademlia, and SFS. Published on 21 Jul 2014
Filecoin is the sister protocol of IPFS. While neither protocol depends on each other, they are perfectly complementary. IPFS handles high performance distribution of objects; Filecoin handles incentivising the world to backup/seed objects.
See also
IPFS is a distributed file system that seeks to connect all computing devices with the same system of files. In some ways, this is similar to the original aims of the Web, but IPFS is actually more similar to a single bittorrent swarm exchanging git objects.
The aim is to have Fedwiki running as a pure Javascript application (no custom server required) and served by IPFS to allow a fully decentralised platform.