As far as I can see, the benefit is the two trees pollinate each other.
I think after they get to a certain size though the stems will become too woody/stiff to continue twisting them together
so I am not sure of the long term benefit.
gardening.stackexchange.com/users/13742/Viv
These 'twisted apple trees' are a fairly new concept, so how they perform over a decade or more will be interesting to see.
Viv is right in that the benefit is you only need one twisted apple, because the varieties are selected so they pollinate one another, and that's an advantage where growing space is at a premium.
Over time, they'll either fuse together or twist themselves, or at least, that's the theory - more info in the link here http://minnesota.cbslocal.com/2015/05/15/new-twisted-trees-produce-apples-on-their-own/
gardening.stackexchange.com/users/1380/Bamboo
Is there a picture we can see?
There is no conclusive way to answer this question without looking at them.
If they are twisted quite well and on purpose, then that seems a bit odd.
If they are twisted just slightly on purpose, that makes sense in a way.
If they are just incidentally twisted, it probably will work out fine, given enough room for both trees to grow next to each other.
If they are quite intertwined, they may have a tendency to strangle each other.
The purposeful twisting sometimes may be done to save space or for the trees to be exotic in look, and share space to produce different fruit simultaneously.
One word of caution though, if this is a big box retailer, at least some of the time, they are not necessarily knowledgeable and usually don't inspect the supplying nursery's inventory.
Many local nurseries will directly bring their product and stack them on the shelves of big box stores like Home Depot, Lowe's, OSH etc.
Sometimes, the retailers employ knowledgeable gardeners they have trained (CA has one such program), but there are not that many of them, and usually even they are tasked with moving product.
So many times, they don't really know what they are selling past a certain level.
This is why dealing with exclusive retailers is helpful.
They too source saplings, etc.
from the same nurseries, but are more knowledgeable typically and will pay a lot more attention in helping you choose high quality saplings, give you advice on planting locations, soil amendments, fertilization, etc.
gardening.stackexchange.com/users/7499/Srihari Yamanoor
I suspect that even with complete knowledge they'd still sell them.
It would take years, maybe even decades for the trunks to do a lot of harm to each other, by which time the sellers reckon you'll have moved/got bored of the trees/pruned them sporadically enough that you blame yourself...
They appear to be a subset of the "family"apple tree; according to the RHS: "These solve the problem of cross-pollination, but can be harder to prune, as the different cultivars often grow at different rates."
I've heard (but can't find a reputable source) that it's common for one of the family to die or be stunted.
I would have though these problems are more likely at least in the short term.
gardening.stackexchange.com/users/7288/Chris H
The 'problem' with this 'braiding' or intertwining of trunks is that it could cause problems with the vascular system
but I've never seen that happen.
They 'grow together' and share vascular systems.
Outside or where there is a lot of wind and when branches rub they aren't able to 'grow together' and the rubbing leaves room for disease to easily infect the plants.
This is very similar to grafting.
Other forms of the same species are grafted right into the host
and then they grow together and have a bark system completely enclosed.
You won't find this braiding happening out of doors with continual movement by the wind.
gardening.stackexchange.com/users/3351/stormy
My friend recently purchased an apple tree twist from a local retailer, and was wondering why retailers sell them that way if they will try to kill each other?  Please correct me if I'm wrong, and they will help each other grow, and not try to kill each other.
If twisted trees will suffocate each other, why do retail stores sell them together?
gardening.stackexchange.com
<trees><design>
gardening.stackexchange.com/questions/29207
gardening.stackexchange.com/users/13136/black thumb
It is so the trees pollinate one another. It could also be to save space. This is a new concept so the trees might not live for a long time. The benefit may be that the two trees pollinate each other. The benefit may be that the two trees pollinate each other. But if they are quite intertwined, they may have a tendency to strangle each other.  
The benefit may be that the two trees pollinate each other. These 'twisted apple trees' are a fairly new concept, with the twisting sometimes done to save space or for the trees to be exotic in look. But if they are quite intertwined, they may have a tendency to strangle each other.  