You have not been using a mesh network if you have been using Apple products. You have been using either an "extended" network if the AirPorts connect together using wireless....or....you have been using a "roaming network" if the AirPorts connect to the network using a wired Ethernet connection.
In an "extended" and "roaming" network the wireless access points use the same wireless network name, same wireless network security and same password. Wireless devices.....in theory at least....connect to the access point with the strongest signal.
Mac laptops seem to be able to do this pretty well, since they will usually automatically "switch" from one access point to another as the laptop moves from one area to another. But iPhone, iPads, most other mobile devices and most PCs will not this very well, if they do it all.
With these devices, it's usually necessary to temporarily turn off the WiFi when the device moves from one area to another, and then turn the WiFi back on......in the hope that the device will now pick up the stronger signal from the closer access point. Works most of the time....but not all of the time.
Mesh networks are designed such that each wireless access point....which is called a "node"......is always in communication with other access points, so the network can "track" devices that are connected much more effectively....and devices can switch access points more effectively. The access points in an Apple system basically ignore each other and leave it up to each wireless device to try to connect to the "best" access point. Not very sophisticated, but it can work OK if users realize the limitations.
Mesh networks were used primarily in commercial applications until recently, but several consumer systems have appeared on the market in the last year or two.
A bit more info here......http://computer.howstuffworks.com/how-wireless-mesh-networks-work.htm