Best-effort delivery describes a network service in which the network does not provide any guarantees that data is delivered or that a user is given a guaranteed quality of service level or a certain priority. In a best-effort network all users obtain best-effort service, meaning that they obtain unspecified variable bit rate and delivery time, depending on the current traffic load.
The postal service delivers letters using a best-effort delivery approach. The delivery of a certain letter is not scheduled in advance - no resources are preallocated in the post office. The mailman will make his "best effort" to try to deliver a message, but the delivery may be delayed if too many letters arrive to a postal office suddenly. The sender is not informed if a letter has been delivered successfully.
Conventional telephone networks are not based on best-effort communication, but on circuit switching. During the connection phase of a new call, resources are reserved in the telephone exchanges, or a busy signal informs the user that the call is blocked due to lack of free capacity. An ongoing phone call can never be interrupted due to overloading of the network, and is guaranteed constant bandwidth.
Book sources 
- Encyclopedia of Networking & Telecommunications ISBN 0-07-212005-3