AP is "access point". It is a wifi signal that the Noop light sends out. You can connect to it's AP signal to set the light up in the App. Kind of like bluetooth, just not quite as easy.
LAN is connecting the light to your wifi network (think it has to be 2.4ghz) and then you connect your phone to the same wifi network to control the lights through the App.
Both have worked for me, but I just find AP mode easier since I have multiple Noops not all running the same schedule, so I just connect to wach light individually.
Hope that helps! Others please chime in if I made an error.