What does DG REX from brittainia on a coin mean?

The motto has changed somewhat over the years, and different abbreviations are used depending on the size of the coin. Basically, it's heavily abbreviated Latin meaning

<monarch's name here>, By the Grace of God <king/queen> of England, and Defender of the Faith.

Before 1948, the motto also included "et Ind. Imp" meaning "and emperor/empress of India"