These cases work by redirecting the electromagnetic radiation (EMR) that is produced by phones, away from the user. All phones produce EMR when connected to the mobile network, and the effect of this energy is measured as a Specific Absorption Rate, or SAR: a measurement describing the radiation absorbed by kilogram of tissue. Government regulations in Australia dictate that all phones in Australia must emit a SAR less than 2 W/kg under the worst case scenario, and while all phones comply, most modern phones emit, at most, only half of this safe level, or approximately 1 W/kg.
I love this case. However, I don't understand what happens to the radiation that must collect under the case; isn't there a burst of radiation when the case is opened? I posted this question but the answers were from people who hadn't thought of that issue; they didn't have the answer, except for one who theorized that the radiation is slowly leaking out the top, bottom, and sides. I assume the case keeps radiation off the hand that holds the case with the phone in it, which is great, but I do wonder about the stored radiation when, for example, I'm listening to a podcast with the case closed, then open it later.

Let’s be honest, we’re addicted to our smartphones. According to an ABC news report, the average person checks their phone 150 times per day, not to mention the other 15 hours per day it sits in your pocket. It’s also nothing new that cell phones emit Electromagnetic Fields/Radiation (EMF/EMR) when it’s glued to the side of our head more than 22 times per day. 
In 2011, the American Cancer Society (ACS) stated that the IARC classification means that there could be some cancer risk associated with radiofrequency radiation, but the evidence is not strong enough to be considered causal and needs to be investigated further. Individuals who are concerned about radiofrequency radiation exposure can limit their exposure, including using an ear piece and limiting cell phone use, particularly among children.
The frequency of radiofrequency electromagnetic radiation ranges from 30 kilohertz (30 kHz, or 30,000 Hz) to 300 gigahertz (300 GHz, or 300 billion Hz). Electromagnetic fields in the radiofrequency range are used for telecommunications applications, including cell phones, televisions, and radio transmissions. The human body absorbs energy from devices that emit radiofrequency electromagnetic radiation. The dose of the absorbed energy is estimated using a measure called the specific absorption rate (SAR), which is expressed in watts per kilogram of body weight.