A pre-arranged visa is exactly what it sounds like: a visa arranged before you got to the airport.
Many countries offer a visa-on-arrival (VOA) under some circumstances. The problem is, the airline cannot be 100% certain you will receive such a visa. And if you land in your destination airport, and that country won't admit you, the airline has to fly you somewhere that will accept you (and then try to bill you later for the flight). If this happens too often, the airline may be fined or even lose its right to fly to that country!
To avoid this, the airline insists on one of two things before they will even let you on their plane:
- paperwork that will (more or less) guarantee that the destination country will accept you
- another ticket, to a country (such as your homeland) that will definitely accept you
That paperwork is often
- a passport from the destination country
- a passport from a country that the destination country has very good ties with
- a passport with a valid visa for the destination country
The check-in clerk usually knows pretty well what kind of paperwork is acceptable (for example, Vietnam has a bizarre "pre-approval letter" that is written entirely in Vietnamese, but clerks recognize it), though they tend to be conservative. For example, supposedly you need a ticket for onward travel to enter Thailand. Thai Immigration never, ever enforces that, but clerks at departure gates in Japan, the Netherlands, and for some reason New Zealand have been known to, forcing traveler to scurry around and purchase last-minute refundable tickets out of the country.
Without proper paperwork, the airline is just not going to let you board. It is too much risk.