What I had understood before was that the airplane carried an Inmarsat satellite transceiver which remained active, even though certain subsystems that use it (notably ACARS) were disabled. While active, the transceiver communicates with the satellite once an hour (the "pings" at 11 minutes past), even if it has no traffic to send. Failing to disable the transceiver in addition to the other systems would have been an oversight on the part of the plane's hijackers, assuming it was hijacked.
Apparently, Inmarsat had available accurate ping timing data. Combined with knowledge of turnaround delays, this would enable them to calculate the plane's distance from the satellite during each ping. That defines an imaginary sphere in space, which intersects with the earth's surface to form a circular locus of where the plane could have been at the time. Presumably, there were eight such ping interactions, ending with the one at 0811 Kuala Lumpur time. There was no 0911 ping, meaning the plane had either crashed or landed and powered off before that time.
And so we had the northern and southern arcs. These were obtained by cropping the circle based on factors such as how far the plane could have flown in the available time, whether or not military radars, if any, had detected the plane, etc.
Now comes the Doppler data. Apparently, Inmarsat also has an accurate read of the plane's transmit frequency. The extent to which this frequency differs from the nominal frequency would indicate the plane's velocity towards or away from the satellite at the time of the ping.
Today, Chris McLaughlin revealed that Inmarsat had studied the Doppler patterns of normal flights in the same region and concluded that the Doppler data for MH370 indicated that the southern arc was the right one. Hopefully, Inmarsat has it right, and the black boxes will be found before their beacon batteries run out.