It's nothing scary — Embr Wave uses plain old temperature to give you personalized thermal relief!
When we talk about "waves of warming or cooling," we're referring to the fact that Embr Wave sends pulses of warming or cooling in a wave rhythm that ramps up and down according to specifically engineered patterns designed to optimize comfort (and battery life) for a given situation. So, the "waves" being sent to your body are the intermittent pulses of thermal sensation, which are physical sensations generated on the wrist using a thermoelectric cooler. (You can read more about how this works here.)
Essentially, we would compare these waves to something like an oscillating fan, which is sending waves of cooling to you as it rotates around the room; or to repeatedly touching a cool glass/warm mug to your wrist over the course of a few minutes.
We've engineered our devices around the way humans feel and respond to temperature, taking thermoreceptor sensory physiology into account to provide pleasant sensations of warmth and cold without using a sizeable amount of energy. The reason we warm and cool in waves is because the human body responds most significantly to changes in temperature. This allows your brain to keep focusing on the local sensation, bringing your body's thermal focus to your wrist and helping you feel more comfortable overall.
Embr Wave is designed, tested, and manufactured to comply with FCC regulations governing radio frequency emissions and considered completely safe to use. In terms of radiation, this would only be from the Bluetooth LE used to communicate with the app and which is standard to most smartphones currently on the market.