How did increased trade lead to more cross-cultural communications between Asia, the Middle East, and Europe between 1000 and 1500 C.E?
Increased trade always lead to more cross-cultural communications because people (especially in the days before container ships and UPS) had to travel away from their homes and meet people in order to trade. This happened in the areas you mention during this time.
During this time, trade between Asia, the Middle East and Europe started out as land trade that came to the Mediterranean and was then shipped to Europe. This was done, for example, via the Silk Road. The presence of this trade (and increases in that trade) led to contacts between cultures such as the one in which Marco Polo went to China.
Because there was more demand for trade, and because for most of this time Europeans could not sail around Africa, there was a need for contacts between Asia, the Middle East, and Europe. More trade meant more traders (and even simply curious travelers) coming into contact with one another in cross-cultural communications.