A bullpen game is a game that is started by a relief pitcher who is not expected to pitch longer than if he were making a regular appearance out of the bullpen. As a result, several pitchers will be required to get through the game. This is different than a game in which a reliever makes a spot start, as in that case he is expected to behave much as a regular starting pitcher and give his team five or six innings of work.
For a long time, bullpen games were only used in the major leagues by teams unable to find an appropriate starting pitcher, either because of a last-minute injury or due to doubleheaders playing havoc with the starting rotation. This was considered a desperate measure and the pitcher that day was derisively referred to as "Johnny Wholestaff" (i.e. every valid body would be called to lend a hand). This began to change in the 2010s. In 2012, the Colorado Rockies briefly toyed with the idea of limiting their starting pitchers to four innings and using just four regular starters. This was part of the team's search for creative solutions to address the pitching challenges caused by high altitude, but the plan was abandoned after a half season when it proved not to have obvious positive results.
The idea received more traction late in 2017 when the Milwaukee Brewers lost their top starter, Jimmy Nelson to an injury while in the middle of a pennant race in September. Instead of using a starter promoted from AAA to replace him, manager Craig Counsell scheduled regular bullpen games in his turn. This worked relatively well and in 2018 the Tampa Bay Rays announced in spring training that they would use the strategy for two of the scheduled five turns in the starting rotation, because of injuries to some of their scheduled starters. This was at first dismissed as a short-term stunt, but the Rays stuck with the plan, and it proved to be quite effective. When career short reliever Sergio Romo started back-to-back games in June, the approach received a lot of media coverage, and most of it was positive given the Rays were exceeding expectations by a wide margin (they ended up winning 90 games). The Rays also introduced the term "opener" for the pitcher given the assignment of beginning the game on the mound, to distinguish him from a traditional starting pitcher.
The strategy received more support in the 2018 Postseason when both the Oakland A's and the Brewers used it in a key game (the Wild Card Game and Game 1 of the NLDS respectively). In both cases, the teams had had a successful season in spite of a sub-par starting rotation and wanted to maximize the impact of having a superlative bullpen. By then, most observers recognized that it was a legitimate strategy, although some conservatives bemoaned it as one more unwanted nail in the coffin of the game they knew and loved. The question was whether it would sweep over major league baseball as defensive shifts had done a few years earlier.