If you would gain life, you gain twice that much life instead.
If an effect would set your life total to a specific number that's higher than your current life total, that effect would cause you to gain life equal to the difference. Boon Reflection will then double the amount of life that effect would cause you to gain. For example, if you have 3 life and an effect says that your life total “becomes 10,” your life total will actually become 17.
In a Two-Headed Giant game, only Boon Reflection's controller is affected by it. If that player's teammate gains life, Boon Reflection will have no effect, even when that life gain is applied to the shared team life total.
The effects of multiple Boon Reflections are cumulative. For example, if you control two Boon Reflections, you'll gain four times the original amount of life. If you control three Boon Reflections, you'll gain eight times the original amount, and so on.