The word babushka technically means "grandmother" in Russian, but the term encompasses much more, a whole mindset and layer of the Russian population. You'll see the babushka everywhere: guarding a museum, running a coat check, patrolling the metro escalators, sweeping Red Square, or suspiciously eyeing your untucked shirt. She may or may not be wearing the brightly flowered head scarf often associated with the word babushka in the West. She may not have grandchildren, or may not be particularly old. But if she has the attitude, she's a babushka.
The babushka considers it her responsibility to keep the world dressed warmly, well-nourished, free of infection, and properly groomed. She'll give you an earful if you're out hatless in winter. She'll berate a young woman for sitting on cold concrete ("It will harm your women's parts, dear"). She'll huff if you hand her a coat to check that's wrinkled or missing a button -- and she may even mend it for you.
Sadly, the skills and traits that made babushkas so crucial to Russia's social fabric are losing their relevance in today's Russia. Fast food and supermarkets are reducing the family's reliance on her cooking and resourceful shopping tricks. Her home remedies are losing their appeal amid a flood of imported medicines. Increased housing options mean fewer and fewer young Russians live with grandma. Men die so much younger than women (male life expectancy is just 60, whereas female life expectancy is 73) that many babushkas are on their own, unable to support themselves on shriveled pensions.
If you speak no Russian, you may not notice the critiques babushkas send in your direction. If you understand Russian or if a babushka upbraids you in English, stay cool. You may find it intrusive, but she wants what's best for you, even if she's never seen you before. In other words, she wants you to feel right at home.