The TSA Approved travel lock standard came about after 9/11. Post 9/11 the US government established the Department of Homeland Security. Under this department Transportation Security Administration agency was set-up or TSA for short.
The TSA was handed the task of Transportation security and primarily that of aviation security following the shortcomings that became obvious post 9/11. The TSA established a standard for padlocks which meant its security officials would be able to open and inspect travel locks with ease using a master key.
Travel Sentry became one of the independent organisations that was formed to authorise and approve travel locks which would be compatible with what the TSA required. These locks became known as TSA locks and are most definitely allowed on international flights. The TSA lock standard was developed in conjunction with the US government.