How did the telegraph help westward expansion in America in the 1800s?

The invention of the telegraph system helped America expand westward because it allowed people who were far away from one another to communicate instantaneously. This was very important for businesses and for the government, and it was a convenience (if rarely used) for regular people. 

Between them, businesses and the government made westward expansion possible.  The most important business in this process was the railroad industry.  The railroad allowed people to move west.  Later, it allowed goods from the West to be shipped relatively easily to the population centers farther east.  The telegraph made this possible.  The telegraph allowed the railroad stations in far apart places to communicate easily.  This allowed them to coordinate the movements of the trains in ways that would have been impossible without instantaneous communication.  The telegraph also made things easier for other kinds of businesses.  It allowed businesses in the West to contact customers in the East very easily. This made it possible for these businesses to make deals with one another, allowing trade between the two regions.  The government was the other part of westward expansion and the telegraph helped it too.  It allowed, for example, military orders to be transmitted quickly down the chain of command.  It allowed local governments to stay in touch with territorial governments.  This made it easier to govern as the nation expanded to the west.

The telegraph also made it at least somewhat easier for regular people to live in the West.  It allowed them, in times of great need, to communicate with loved ones back East.  It allowed them to have newspapers that were relatively up-to-date because the newspapers got news via telegraph.  It allowed the settlers to feel more connected to the country as a whole. 

In all of these ways, the telegraph helped the United States expand westward during the middle-to-late 1800s.