Courier is said to have originated from the Latin word 'currere' which means 'to run'. Couriers were used back in the Ancient Rome where these network runners would have run between two points in order to deliver a package or message.
For delivering messages or packages across long distances, the couriers back in those days used a relay system where a runner would run for a day or so with the message and deliver it to an another runner waiting at a checkpoint who would then set off with the message.
The most famous of these runners was a Greek courier called Pheidippides who as per legends ran 40 kilometres from Marathon to Athens to inform people of a Greek victory over the Persians in 490 BCE and then collapsed and died. In fact, Marathon is named as such in the memory of this event.