The Messenger Service was one of the only two Shire-services (the other being the Watch). It was the system used in the Shire for its inhabitants to communicate with each other. By this way, along with the Quick Post (which was probably a part of the Service), letters and news was passed between the four Farthings.
The Shire-hobbits wrote constantly to all their friends, so the Service was much busier than the other, the Watch; and numerous Hobbits worked as Messengers (in contrast to the only twelve Shirriffs and the Bounders).
In the days leading to Bilbo's Farewell Party, Bilbo Baggins sent hundreds of invitations all around Hobbiton and Bywater, followed by hundreds of responses; the respective post-offices were blocked or overwhelmed, and volunteer postmen came to assist.