The following quote from Cochran and Cochran (2000) provides some explanation for the transitions, and the notation used to describe them, included in the data tables. Notationally, this quote corresponds to the original publication with two exceptions: "Pi" is used to represent the Greek capital pi symbol; and "Sigma" is used to represent the Greek capital sigma symbol.
...the digital tables will be entirely in ASCII characters and will not use any sub- or superscipts; they can be utilized on any computer without having to deal with embedded special characters. The tables are in fixed format. For most molecules, the electronic transitions are listed by their letter designations (A, B, X) instead of their term designations. For C2, we use the more common names of Swan and Phillips, where the Swan band is the d3Pig a3Piu band and the Phillips is the A1Piu X1Sigmag+ band. As vibrational transitions carry designations with different forms for diatomic and polyatomic molecules, those transitions are listed in the manner appropriate for each molecule. In all cases, the upper state is listed first, then the lower state. For the rotational transitions, the designations are very dependent on the individual molecule, since some just have P-, Q-, and R-branches, some, such as CN AX, have branches such as P12, and some, such as CH, have branches such as RQ21f e (which is listed as "^RQ21fe" in plain ASCII). Molecules such as NH2 and H2O+ have rotational states which are designated with three quantum numbers of the form N'K'aK'c N"K"aK"c. The NH2 and H2O+ rotational states are separated into F1 and F2 components. We have not included these designations in our tables.