By default the ESP8266 has it’s own unique AP. I.e. when you power it on out-of box and start their API, it starts in host-mode running its own DHCP server. You can find it by looking for a wifi ...

A lot of people have used ESP8266 to add inexpensive WiFi connectivity to their projects, but [Oscar] decided to take it one step further and program an Arduino over WiFi with the ESP8266. [Oscar] … ...