Is there onboard memory? Or does this always have to be connected to Wifi to work?

All of the products in the Lascar Wireless-Alert series only serve to send an alarm of a specific condition. They do not record or retain data. They require a WIFI connection to be able to send out an alert notification. For this specific device it would send an email to you each time a door, window, etc.. is opened. They can be set up to also send you a weekly summary of events, but no data is retained on the device itself.