Translation:He spoke without a pause for ten minutes.
In California "without stopping" for sure. You might see regional differences... perhaps "without pause" is used more in England, for example.
I also see some discussion below about using the word "nonstop" which I think absolutely SHOULD be accepted. It would be very normal to say "He spoke nonstop for 10 minutes"
A common idiom, yes. Examples "I've been working nonstop all morning". "He spoke nonstop for 10 minutes" "They've been hanging out nonstop since we got here" etc etc.
It means to continue without any pauses or breaks. A very common usage is related to travel as well. "Driving nonstop" or "A nonstop flight".