International trade in a simplified argument is necessary to boost prosperity because it allows nations to use their absolute and comparative advantages to the maximum extent.
Industries of all nations can export the products and services that they can deliver at the lowest cost and for the highest price and can import products and services that other nations can deliver to them at the lowest price. This benefits all the parties involved in trade.
International trade forces industries of all nations to become as efficient as they can, thereby reducing costs. This coupled with the fact that they have access to markets where their products can give them the highest price ensures very high profitability.
The increase in profitability would imply an increase in prosperity.