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A bit more seriously, though - They are very likely doing this largely because they found it difficult to make agreements with their suppliers (studios) for the two portions of their business separately.
For instance, studios allow netflix to press their own DVDs and Blu-rays at a steep discount based on profit sharing. In other words they give the studio a few pennies from each "rental" rather than $20 per copy - this means they can press a few thousand copies of popular movies, but only pay for the actual usage of those disks, rather than a fixed cost per disk - it also means less loss when a disk is scratched, lost, or stolen. Further it reduces theft because the discs no longer have the special features - one of the reasons the studios allow such a discount, by segmenting the rental market away from the purchase market.
To the point, though, they previously were happy to include "streaming" in the same contracts they made for their disc pressing. In fact they were probably able to set the contract up in their favor since streaming would have similar cost/usage ratio.
Well, the studios now have the upper hand in terms of streaming (more streaming distributors, such as cable companies, telco, etc) and they want to charge more.
It's not longer in netflix best interest to combine the contracts, but of course the studios will make their demands anyway. By separating the companies, netflix is specifically making certain the contracts don't affect each other (which is also a big deal since the physical plants of DVD sending and network operations are differently expensed anyway, and should be accounted differently).
So there are a number of corporate, legal, and financial reasons to split the two apart.
But it's a very "corporate" move that has no benefit for the consumers.
