You have to save those bools somewhere outside of the game, like some save file and when you start up the game again it would read the file and set the bool values according to what you have in the file

Excuse me, can you explain it more detail ? How can I save bools variable outside the game ?

He mean saving the game state in a database or in a file before you quit the game. And then when the user start the game you load the file and check what levels are unlocked

You can use the function PlayerPrefs, it is pretty easy! give it a try... Basically, you can save or load whatever floats, strings or int's you want into a default file that UnityEngine creates on the host computer.

http://docs.unity3d.com/Documentation/ScriptReference/PlayerPrefs.html

thanks, I'll try this. But, can it applied for mobile game ?