when you search google for "barack obama wikidata", you get:
Barack Obama - Wikidata
7 days ago - "The president's symptoms are consistent with soft tissue inflammation related to acid reflux and will be treated accordingly," Obama's doctor, ...
(pulling the text from a quote within a reference of the first statement on his item, instead of using the item description)
not sure it would always work, but looks like we could add a meta description in the header of the page that might provide more useful hint for the search engine.
"new york wikidata" is better, giving:
New York City - Wikidata
7 days ago - largest city in New York and the United States of America . Also known as: NYC; New York; City of New York; New York, New York; The Big ...