Why were trijets so popular back then 20 years ago?

Skipper7 is correct. Back then planes had to have enough power for extended range when flying over water. Now with reliability and power up. Aircraft can fly whats called ETOPS, extended twin ops. The reliability of the aircraft must be tracked and maintained to fly over water, some 757's and 767's are ETOPS but not all. Also you cannot use parts off of a non etops aircraft on ETOPS its a highly regulated operation. The fewer the engines the cheaper the operational cost.