What does the following mean suggested pressure of the rear tire is 7 to 8 atmospheres?

An atmosphere is a measurment of pressure with one atmosphere being equal to the air pressure at sea level, approximately 15 P.S.I. 7 to 8 atmospheres would be approximately 105 to 120 Pounds Per Square Inch of pressure.

Im guessing that tyre is a typo and is supposed to be a "tire" of some vehicle. Anyway the suggested pressure is the ideal pressure inside your rear tires. 1 ATM (or atmopshere) is the standard atmospheric pressure at sea level. Just look up the conversion rates online between "ATM" and the units of measurement on your tire pressure gauge. Some of these units might be kPa (kilo pascals), torr, or mm/Hg (or millimeters Mercury).