DMR stands for Digital Mobile Radio and uses the Motorola TRBO protocol for communications. Like other digital modes such as D-Star, C4FM and APCO P25, the TRBO protocol converts your voice into a digital form and sends it out via RF (with other bits of information included) and allows you to communicate to other DMR radios and also DMR repeaters, which are networked together around the world via the internet.
What makes DMR stand out from some of the other digital modes is that it utilizes TDMA (Time-Division Multiple Access) to divide a single frequency into 2 distinct “channels” or time slots. By doing this, you can have two conversations going on at the SAME TIME, using one frequency.