I got one of these offers today for the first time as well. The offer was $20 to switch an evening OAK-BUR flight on a Thursday to a selection of flights earlier on Thursday, morning through mid-afternoon on Wednesday, or one choice on Saturday afternoon. All flights into BUR are on 700s, so the reason is clearly not an aircraft swap. I find the, "for a limited time, we'll wave any fare difference..." particularly amusing -- as if I was so desperate to switch my evening flight to the day before at 6:00am!
Currently, the lowest available fare on OAK-BUR flights earlier in the day is $204, and this particular flight is selling for $324. As some have suggested, what I think is happening here is that WN wants to get some seats from volunteers so that it has enough seats available to sell for a premium to high fare, last minute-booking business travelers. WN put out a very aggressive Q4 forecast that all the analysts didn't believe, and I think management is desperately trying new things to hit those targets. This seems to me to be one more item in their new toolkit.
Two other thoughts: (1) I think they realize now that they may have sold too many tickets too cheaply to discretionary travelers in the past few months as they've worked out their basic economy strategy and are going to try to use this initiative to recoup some of the fare loss and (2) I think they're going to test their customers price sensitivity for offers. $20 seems laughable, but if there aren't enough takers, perhaps they'll pump if up. If they could get a fare premium of $100+ on a flight like this, they could certainly afford to (with the caveat that the recouped seat might not sell, but I'm sure they have a probability-adjusted estimate of what it would sell for).