When I talk about under-functioning, I mean the "normal" doing less of something because the other does more of it, which, to a degree, is perfectly normal in any couple ("couple" meaning any two people functioning together, i.e. at home or in the workplace etc).
Learned helplessness is pushing the concept of under-functioning to its terrifying extreme: when one becomes helpless in certain areas, to the point of disability.
Let me start off with a couple of examples:
A friend found out the hard way that leaving all the financials for her husband to manage meant financial ruin when she discovered that he had gambled away both their fortunes.
Another one: my mother-in-law never learned to drive, as her husband was always driving (and for most of her girlfriends that was the norm too, a generational thing I guess). Then she saw what happened when one of their husbands died: the widow suddenly was more or less stuck at home, depending on her friends and children to go anywhere. But my mother-in-law being the opposite of a helpless lady, she decided at age 50 to learn how to drive, and has been successfully driving for the last 25 years. Yet most of her girlfriends are still trapped, because they chose the "safe" path - sticking to what they knew.
Now, before you think only women suffer from learned helplessness, spare a thought for all those husbands who leave their whole social life to their wives to organise, to the point where they don't have any friends of their own. In case of divorce, they end up terrifyingly alone.
But there is more to learned helplessness than just a lack of independence: it is about creating a belief that you are incapable to do something, when really you would be quite able if you made the effort (like my mother-in-law).
Now why would anyone want to become or stay helpless?
Because there often is an emotional side to the equation: both the over-functioning and the helpless bind themselves closer unto the other, making it a co-dependant relationship, where both can only exist with and through the other.
What can you do to change this dynamic?
Start with becoming aware on the areas in which you may have developed helplessness or taken over in your relationship.
Accept that there might be fear - fear of failure in the new endeavour, or fear of being abandoned if you stopped being either so "necessary" or so helpless.
Talk about it with your partner, in order to separate the emotional undercurrent from the practical issue at hand (by the way, for the practical side of things, outsource them, don't try and teach your partner yourself).
Untangling a co-dependant relationship will take time and effort, and courage.
But the reward is great: a relationship of two strong, independent people who choose to be together rather than stay together because they fear being alone.