Regular difficulty
Regular difficulty is the difficulty level at which any eligible closed team across the whole range of skill levels can play meaningful games against any other eligible team. (i.e.: A regular-difficulty high school set will have a distribution, selection of clues/answers, etc. that allows the more knowledgeable high school team in a given match to consistently win, regardless of whether it's a match between weak teams, average teams, or strong teams.)
More generally, regular difficulty tournaments must be more difficult than novice and easy tournaments on one hand (or else games between highly-skilled teams will feature too many buzzer races on early clues) and less difficult than hard tournaments or national championships (or else games between average and below-average teams will feature too many dead tossups, buzzer races on late clues, and situations where luck of the draw on bonuses determines the victor). Regular tournaments must also avoid especially-wild fluctuations in difficulty from question to question, from category to category, and from packet to packet.
High School
In high school quizbowl, the range of regular difficulty is usually defined by the difficulty level of NAQT Invitational Series sets, as well as independently produced mACF sets such as LIST and RAFT. These sets are designed to produce consistent, meaningful aggregate results for all high-school matchups. GrogerRanks uses a regular-difficulty set—usually an IS set—as the benchmark for its powers/game and PPB adjustments when computing teams' scores.
College
In college quizbowl, the barometer for regular difficulty has traditionally been set by ACF Regionals. Examples of recent tournaments that successfully achieved regular difficulty without overshooting include ACF Regionals from 2008 to the present, Penn-ance, and the Division I SCT from 2012 to the present. More discussion of what collegiate regular difficulty consists of, and how to properly write questions for it, can be found here, here, and here.
More recently, many community figures such as Eric Mukherjee have advocated for the redefinition of college regular difficulty to be the level of EFT (i.e. "two-dot" difficulty on the college quiz bowl calendar's difficulty scale), in order to lessen the perceived difficulty of collegiate quizbowl to newer players. However, older members of the community have largely resisted this change, resulting in much confusion surrounding the term's meaning. This has been exacerbated by the fact that the abbreviation "regs" may refer to either "Regionals" or "regular," and has led to a decline in the usage of the term "regular difficulty" among the college quizbowl community.