Steam has been important in world history for two main reasons. These are industry and transportation. By providing power for factories and transport systems, steam made the Industrial Revolution possible.
Before steam, factories could only exist in places with rivers big enough to power mills. Steam did away with this requirement and allowed factories to be sited wherever was convenient. Before steam, large loads could only be transported with the current on rivers, by draft animals on canals, or using the power of wind on the ocean. With steam, large loads could be moved over water in any direction and in most wind conditions. Steam even allowed railroads to be built, thus making it possible to move large loads across land relatively easily.
In these ways, the harnessing of steam made the Industrial Revolution possible and changed the world forever.