When Insomnia is enabled the device will not sleep, meaning that background applications will keep running and WiFi will stay connected when the screen is off.
An icon appears in the status bar to remind you that Insomnia is enabled.
This version of Insonmia runs as a SpringBoard tweak meaning it survives reboots and resprings.
If you turn on the schedule (Insomnia Pro only) then Insomnia will only be active between the two times specified. It will wake up at the start time and sleep at the end time. This feature only wakes up the device from standby, if the device has been powered down completely it won't power up for the schedule. WiFi won't wake up at schedule start but this problem is being worked on.
Insomnia causes the battery to drain because the CPU is running all the time, usually it sleeps a few seconds after the screen goes off. Insomnia has been designed to override that behaviour but at the cost of battery life. It may only last a few hours so short term use is recommended.
If you have push notifications on or periodic email checking your device will wake up periodically.