In a connection-oriented communication, the data is guaranteed to be delivered. Any data that is not received by the destination is re-sent by the sender. Communication between the sender and receiver does not stop until the transmission has been verified. Off course all this requires a higher overhead, so connection-oriented communication usually requires higher bandwidth.
On the other hand, connectionless communication offers only best effort delivery because the information sent does not have any type of conformation that data has been received. If an error in transmission happens there is no mechanism to resend the data, In other words there is no guarantee that the data will be received correctly. Obviously this requires less overhead/bandwidth than connection-oriented.
Usually, this terminology can be applied on either the datalink layer and/or transport layer and the way it's implemented relates to what protocols are used. For example, In datalink layer, Frame Relay is considered connection oriented while 802.2 protocol can provide both connection-oriented and connectionless communication.
These examples helped me:
Say you have some information to communicate to a person in the next town:-
Connectionless - Like putting the information in an envelope, tossing it in the post and not knowing or having any control from that point on whether it arrives or not.
Connection-Oriented - You call the person on the phone, and once you have a connection and he's there you give him the information and ask him did he get it ok or does he want any part of it repeated.
The first is like UDP, the second is like TCP