An enduring impact is a change made by a people that impacts the world we live in today. The quote "seeing the world with new eyes" refers to being able to see Rome in the world we live in today based on its enduring impacts.
The picture below shows concrete from the USA. Concrete roads were an enduring impact of the Romans. Concrete is the mixture of ash, lime and water. The first roads were for military transport. This is important because without the Romans, we would not have concrete like we do today.
The photo gallery below shows some more enduring impacts of ancient Rome. These pictures are taken from the United States of America today, but the ideas shown in this picture were originated by the Romans.