In economic commentary, there is typically a very strong focus on GDP – the value of production – as a summary of national material progress. There is also quite rightly an emphasis on lifting productivity – real GDP per hour worked – as the source of our growth of material living standards.
For open economies, though, our standard of living is affected not just by the physical output we can obtain from our resources of labour and capital, but also by the purchasing power of that output over things we want to have from the rest of the world. This is what the terms of trade is measuring.