I think the experience of new cultures is a huge benefit of travel. People see things they otherwise would not see and are opened to new perspectives. Traveling is a great way to see that not everyone does things the way I do it, and not everyone believes the same things I do. Additionally, our minds are broadened by the simple absorption of information, images, memories, etc.
Beyond that, travel can broaden the mind by simply being a challenging thing that causes us to think critically and problem solve. When we travel, we have to figure out a budget, map out an itinerary, and do many other things that require a great deal of thought and planning.