That means it is acidic, much more than the normal rainfall reading of 5.6 which is still acidic. The scale is 0-14. 0 being strongest Acid, 14 being strongest base and 7 being neutral.
I would test my your rain water to see what it reads direct collected. Get a reading and then aerate it for 24 hours and check it again. Lawn and garden, pet stores and pool stores should have fairly cheap and easy to use pH test kits. One recommendation, get a liquid test kit and not strips. My work with aquarium fish has taught me a hard lesson on the accuracy of strips compared to liquid testing.
What a pH of 4 means to you being able to use it for your animals, I wish I could help there but I do not know.
I have used rain water for 9 years for aquariums, frogs, insects and rodents and I have never seen a negative effect from it.