They're not directly equivalent. REM stands for "roentgen equivalent man", which is to say, it's Roentgen modified by a factor which accounts for how much dose an actual human would absorb. The absorbed dose differs depending on the type of radiation involved. If we assume that the radiation involved is mostly gamma, the modifying factor is "1", so this would be equivalent to 81.6 microrem/hour.
As a general idea of how much radiation this is, background radiation in many parts of the United States is about 10 microroentgen/hour. So this is about 8 times higher than average background radiation. If you live in an area at a high elevation (less air above you to block the sun and cosmic rays) or in an area with a lot of granite or other naturally radioactive rock, your dose will be higher. The dose being recorded by that counter is actually on a par with living in Denver (high, granite-y).
Of course, that counter may not be recording anything like the highest dose in the area.
