There is an extensive body of work on this subject and most can easily be found if you searched this forum. It is apparent that due to the cross section of an elbow flattening during bending [ovalising], that a bend is more flexible than a piece of pipe [same OD, wall thk etc] of the same centerline length. The flexibility factor tells you how much more flexilble the bend is when compared to that notional piece of pipe. ie the bigger the flexibility factor, the more flexible the bend is.
Since adding very stiff fittings to the end of the bend, such as flanges, will reduce the ovalising present in the bend, thus making the bend less flexible. The "correction factors" are used to simplify the calculation of this additional stiffness. Since the 'flanged' bend is stiffer than the unflanged bend, the calculated flexibity factor needs to be reduced [less flexible]. They are "reduction factors" as they are used to reduce the flexibility factor.
Ultimately these all correspond to how the structure behaves under loading and also lead directly to stress intensification factors.
Please have a look at your copy of B31.3 [if you have one]. It's all in there. Alternatively I believe the original work was done by Markl if you can get a copy of that. Some newer codes also publish these factors for reducers for all sorts of geometry beyound the usual branch fittings and elbows commonly seen.
This is really basic stuff, but since nobody was ever born a complete stress engineer, perhaps if you are starting off in the field a few words explaining that at the beginning of your posts will give a better response. There has certainly been an increase in 'basic' questions being asked here recently. Everyone is willing to help students. No-one wants to help 'chancers'.