The telegraph brought about the era of instant telecommunication between humans. It was a millennial dream that had not been able to be turned into a reality until its inception. It first boosted the economy since it allowed commercial agents such as investors, producers, distributors and intermediaries to be in immediate contact across long distances which helped to exponentially increase trade by allowing them to coordinate the production, delivery and sale of products and services a lot more efficiently by reducing the time that it normally took to, communicate between parties.
Considering that as imperialist countries expanded their empires, they came across not only new sources of raw materials and labor they created new needs by the imperative of setting up suitable living areas and their necessary infrastructure. As settlers came to live in a un-industrialized and technologically deprived area they needed to coordinate quickly and efficiently with their metropolitan counterparts in order to organize the flow of workers, products and supplies to and from the colonies in order to make the new colonized areas livable for them and economically viable.
In military terms, the telegraph allowed for an intensified degree of efficiency and rapidity in the communication of potential and imminent military threats (be it by insurgent forces or rival military powers). This allowed them to appropriately allocate military resources and personal to the areas that most needed it.
In political terms, every order or regulation stemming from the metropolitan authorities was conveyed a lot faster through the telegraph, which favored its swift implementation and asserted colonial authority.
A great example of the importance of the telegraph is the painting American Progress by John Gast. You will quickly notice the telegraph lines depicted in it.