A mesh network is a network topology in which each node (called a mesh node) relays data for the network. All nodes cooperate in the distribution of data in the network. (Wikipedia Article)
Mesh networks can be connected in various ways, but are quite often connected using WiFi. They are a form of topology that attempts to be self correcting in the event that one or more nodes are down.
The goal for the Mesh Netwoking project is to learn about, and potentially develope and/or deploy, mesh networks. Mesh networking has great potential in any situation where standard network conenctivity is either inconvenient or just not available. Mixed with various anonymizing technology, it can potentially be used to support secured communications as well.
It may very well be among the technology needed to create a kind of backup internet if the need arises.