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.
In high school quizbowl, the range of regular difficulty is usually defined by the difficulty level of NAQT Invitational Series sets and HSAPQ Tournament sets, which are designed to produce consistent, meaningful aggregate results for all high school matchups.
In college quizbowl, the barometer for regular difficulty is usually set by ACF Regionals. Examples of recent tournaments that successfully achieved regular difficulty without overshooting inlcude 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.