Here is the full sentence:
You’re from Orinda, your father’s in commercial real estate and your mother’s 10 years sober.
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Hasn't had a (alcoholic) drink for ten years - presumably was an alcoholic and is now clean.
In the context presumably intended as a slur on the sort of person whose parents sell real estate and are recovering alcholics!
To be "10 years sober" means that the person has not used alcohol for 10 years.
You can also say, "I've been clean for 10 years" to mean you haven't used drugs in 10 years.
People often use the two terms together, "clean and sober for 10 years."
In the reported sentence sober means "not affected by alcohol; not drunk."
Other meanings of sober are: