In a traditional wireless LAN topology, each Access Point (or node) is tied directly to the wired LAN.  However, most wireless access points only cover distances up to 300 feet, so you can't provide coverage very far from your nearest available wired network connection.

Mesh Networks don't rely on as many direct connections to the wired network.  Instead, one Access Point can hop to one or more other Access Points (up to three hops) before making this connection. 

The benefit is that you can cover larger areas without having to extend your wired network.  Additionally, Access Points can have multiple paths they can take to get to the wired network.  If you lose an access point, traffic from other access points will re-route to prevent other nodes from failing.

Single vs. Dual Radios

Some mesh networks use a single radio for the wireless access and the backhaul (routing to the wired network).  The total available bandwidth of the each radio at the access point is shared between these two functions.

Other mesh networks use two different radios for the two functions.  This design provides a faster network with more user capacity.

Mobile Applications

Many mesh networks don't work well for mobile users when traveling greater than about 20 mph.  Each access point only covers a very small geography, and the mobile user is quickly moving from one access point to another.  The technology available today doesn't "hand-off" fast enough between access points to accommodate faster moving vehicles.  Newer mesh products claim to overcome these problems.