I bought some bare root blackberries from a reputable nursery and in the instructions they said to "prune roots 1/2" to 1" with sharp pruning shears" before planting.
What purpose does this serve?
It's because when they dig the plant, the dirty ragged cut the digger leaves on the roots is left when the plant goes to storage. The roots on your plant used to be a lot longer, but (of course) when they were dug, the roots had to be cut.
That's why trimming off the last 1/2 - 1 inches of root can be good for the plant, sort of like trimming dead/ragged stubs on a branch. The roots can then branch from the end of the cut, more than if you left the old ends on. Also cut any broken or stripped roots behind the point of damage.
It's not an absolutely necessary step, and it does lose you minimal amounts of roots, but it's more of a long-term root-structure helper. I've seen plantations grow equally well with and without this treatment, but I usually do it, because I know it helps the plant develop a better root system (not stronger, necessarily, but a better shape)
I have no idea, never heard of it, usually the only time you need to trim roots is if they are damaged, when you may take off those parts affected. It is, though, common to be advised to prune back the canes (topgrowth) to 6-8 inches if this has not been done prior to despatch. I certainly wouldn't advise cutting back roots for plants which are going to be growing in open ground, particularly not at this time of year (Spring). There's a possible argument for doing it in autumn, to force the plant to put out new roots during the dormant topgrowth time, which isn't an argument I'd subscribe to anyway, but it doesn't make any sense to do it now, really - any plant is only as good as its roots.
I'd be inclined to ask the 'reputable nursery' why they've suggested it, I'd certainly like to know!
It encourages new root growth which is important to the plant's survival in the first several weeks. It's common for bare-root stock of many sorts to suggest trimming the roots.
If you don't trim the roots, the plant has less impetus to push out fresh roots. That's all.
It's like pruning the tops, if you don't prune you get leggy plants with less fresh foliage, same principle applies to the roots.