Trade spreads ideas and culture because it involves people moving from place to place around the world as they trade. As they move, they (and the people they meet) come into contact with new ideas and cultural practices.
When discussing this, we should specify that trade does not spread ideas and culture nearly as much as it did centuries ago. Today, trade is a rather impersonal business. The United States imports huge amounts of goods from China without being exposed to Chinese culture and ideas because trade is not really done by people anymore. Ships are loaded in China by Chinese people. They arrive in the US, where they are unloaded by Americans. You do not have Americans going to China to buy the products or large groups of Chinese coming to the US to sell them.
Centuries ago, things were different. For example, goods would be brought across the Middle East by camel caravans. This meant that relatively large numbers of people would travel along with the goods. They went slowly, stopping often. When they stopped, they would interact with local people. There would be exchanges of ideas. People would see things like how other cultures cooked, what clothes they wore, and what religious ideas they believed in. In those times, trade was a much more personal business that involved many people travelling. As they traveled, they exposed the people they met to their own culture. At the same time, they were exposed to the cultures of the places through which they traveled. In these ways, trade spread ideas and culture, making it an important force in world history.