Exclude / Exclusion / Reset a device / Remove a device: These all mean the same thing and refer to resetting a device, or removing it from whatever Z-Wave network it is currently in. See Reset Node
Include / Inclusion / Pair / Add Device: These all mean the same thing and refer to adding a new device to the current Z-Wave network stored in the primary controller.
Mesh network: The range that a Z-Wave can transmit information to another Z-Wave device is between 30 and 100 feet. However, Z-Wave is a mesh network, meaning if there are nodes in between, they can act as relays or repeaters. In this way, if you have 5 Z-Wave devices, each is 30' apart, and the 2 furthest are 120' feet apart, the 2 furthest nodes can still talk to each other because the 3 nodes in the middle act as repeaters. Z-Wave supports a maximum of 4 hops, meaning there can be up to 4 repeaters.
Primary Controller: In a Z-Wave network, there needs to be 1 device that is designated as the "Primary" controller. This is the device that keeps a database of all the other Z-Wave devices in your network. The primary controller also has responsibility for ensuring the health of your Z-Wave network by regularly checking what nodes are working and what other nodes are close to them to act as relay points. By default, Vera comes as your primary controller, and you add your other Z-Wave devices to Vera. If you already have another primary controller and don't want to rebuild your Z-Wave network, Vera can become a secondary controller. On Vera's devices, Z-Wave options page it shows which role Vera has.
Replication / Replicating, copying, or transferring a Z-Wave network, adding a secondary controller: These mean the same thing and refer to sending a copy of the master database of Z-Wave devices contained in the primary controller to some new, secondary controller, which will now become part of the Z-Wave network and have a list of all the other Z-Wave devices so it can control them too.