This is pidan 皮蛋, also known as century eggs or preserved eggs. They are most commonly made with duck eggs. Some might call them hundred-year eggs or thousand-year eggs. In 2011 the viewers/readers of one major US media voted pidan the most “disgusting” dish/food. Ok, this food might not sound or look appealing to you, but to Chinese people, this food incorporates with culture and heritage. We shouldn’t mock a cultural food that millions and billions of people have enjoyed for hundred of years. Well, in the future when you are offered unfamiliar food, how about saying “thank you, it’s not for me”, or “I am not a fan of this”, instead of making a face “this is disgusting”. Or explore new things, try it, at least once, because I know some people (not from China) love “strange” Chinese food like pidan.
Check out a story on a pidan maker in China by Goldthread via this link. I hope this video answers your questions about pidan.