What is a default gateway address?

A default gateway address is only applicable when you need two different networks to communicate with one another, and a router/gateway is added to the system. 

What the gateway address does is reserve an IP address for the gateway/router that will be included as the intermediary and lets the device know that it is there.

Here is an example:

You have two devices on two different networks and you want them to communicate.

You include a router between them to establish a connection. The router will need two different IP addresses in order to be able to communicate with both networks. The router's addresses are then given to device A and B so they know who the router is.