it's talking about ignorance with regard to specific application.
for example people who try to argue the earth is flat using physics. the position they argue from is that they consider themselves to be far more competent than practically everyone else at comprehending physics, but the reality is that they are so incompetent at physics that they are incapable of realizing how poor their arguments are.
for another example, people may argue that Jesus was 'only a man' who achieved some sort of enlightenment or glorification by perfectly obeying Judaic law, or perhaps that He became 'exalted' to godhood but was otherwise no different than any ordinary human apart from His obedient works. they may argue this using scripture, and think of themselves as highly competent Biblical scholars for doing so -- but they lack the very competence in studying and understanding the scripture that would show them how wrong their doctrine is.
the effect demonstrated by the two researchers is that people can be basically so bad at something that they don't realize how bad they are at it, because they aren't even good enough at it to understand that they are actually very terrible at it ((whatever 'it' may be)) -- and somehow their pride gets in the way of them seeing they in fact have no reason whatsoever to be proud.
a third example - we have some kittens, and one of them plays candy crush on our ipad. she has no idea how terrible she is at it, she just whacks the screen. she thinks she's doing great - i mean, she whacks the screen, and stuff happens - must be good, right? she thinks. because she doesn't know enough about the game to realize she's actually awful at it.
that doesn't mean she's not good at other stuff -- just that at this one thing she's not competent enough to realize she's incompetent, yet she's very proud of herself for what she does accomplish, even though what she actually accomplishes is wrecking her human "mommy's" winning streak.
