In which way was communication by telegraph an improvement over communication by mail

Speed. Mail delivery even now takes 3 or 4 days by ordinary snail mail (that's why it is called snail mail) to get from one side of the country to the other and that's major city to major city. Telegraph communication made it simpler to communicate directly very quickly with whomever you wanted to contact. Now the problem became how many messages could be sent at once. There still was no quick or inexpensive way to deal with parcels. That's what trains were for.