A mesh network is where you have a number of access points and they are all communicating with each other and spreading the wireless signal from them. This in turn gives better coverage through your network area.
There are a number of wireless mesh network devices now available. They usually have three or more units in them and then you set up the units through where you want the signal sent. Then since they are near each other they are all sending out and sharing back and forth and give you strong signals over a larger area.
The principal in mesh networks is similar to how your cellular service works so you bounce from tower to tower and as a user never realize you have changed receiving points to the cellular network.
With the mesh networks used at home I am seeing people report better service in areas further from the main point such as into the basement or by the swimming pool.
The mesh network is definitely something to consider when you need a new wireless router if what you have currently leaves areas you want reception with poor or not adequate service.