IN TODAY: We have new circuit allotments for the justices: Sotomayor adds the 6th (to the 10th, which she already had), Kavanaugh has the 7th, Kagan has the 9th. (The Chief had taken on the 9th since Kennedy's retirement, and Kagan previously had the 6th and 7th.) #SCOTUS 
The main reason, now, why the circuit allotments matter is that the justice assigned to a circuit receives applications in cases out of that circuit, mainly attempts to stay lower court rulings pending further appeals and requests for stays of execution.
Justices almost always refer full consideration of substantive decisions on applications to the full court. There have been a few exceptions in recent years, but mainly when it was a recurring matter and the outcome was pretty clear/likely.
This makes sense because if a single justice denies an application, the party, under the court's rules (22.4), could technically resubmit the request to another justice — although the practice is "not favored" generally, per the rules.
Another reason, more applicable to practicing lawyers, why circuit justices can matter (particularly because, under the court's rules, requests for extensions of time cannot be resubmitted to another justice):
A compelling historic example, relating to the bombing in Cambodia:
Here was Justice Marshall, on August 1: supreme.justia.com/cases/federal/…
And Justice Douglas, later that same week: supreme.justia.com/cases/federal/…
And Justice Douglas, later that same week: supreme.justia.com/cases/federal/…
Note: With the 9th Circuit changeup, it is not immediately clear what happens to the pending application in the kids' climate change case. The application was submitted to Roberts when he oversaw the 9th, but now that circuit has been reassigned to Kagan.
We’ve not gotten anything yet on the climate change case stay application — not a call for a response or an order on the request for an “administrative stay” while the stay application is considered. (The order from Ginsburg in the Census case, in contrast, came that same day.)
