Airside is generally the area beyond security and/or passport control. In other words, the area accesible only to airport staff and passengers holding valid boarding cards for imminent travel. It may also be called the sterile area, as presumably everyone in the area has been security checked, a requirement given everyone has access to flights and aircraft. The airside area includes the duty free shops and often the lounges in most airports.
The landside area is accesible to the general public, including those not traveling. It includes check-in and ticketing desks and is not considered a "secure" area in the same sense as the airside area.
In the US before 9/11, the general public had access to the airside area, something that I never really understood. Now it is like most places: the airside area is accesible only to passengers.
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