For an American, this is a tough question to answer. In the US, when someone asks this question, the answer often involves cultural heritage of one of our strains of ancestry rather than dominant American culture. We do not see US culture as culture but as the default against which our ancestors’ cultures play.

For example, people in the US talk in terms of hyphenates. They are Greek-American, Polish-American. African-American. Or they say “I have German ancestry”. The people who say this often experience their cultural heritage at holidays or in public festivals, or they live in an enclave where many people with that ancestry live. They notice differences from their classmates growing up; their classmates didn’t eat olebollen or pickled herring on holiday.
Which brings me to what I like about my cultural heritage. I am, like many Americans, a ‘mutt’. I have German, Dutch, Polish and Irish on Mom’s side and French, German, and probably Welsh on Dad’s (among others), according to Ancestry.com. Of these, I’m most cognizant of the German/Polish on Mom’s side and the French on Dad’s. The German/Polish on Mom’s side was a matriarchy of sorts that tried to ignore the Polish ancestry for bewildering reasons. The French on Dad’s side was what is known as ‘trapper French’, or the Canadian French who lived through hunting, trapping, and trading wild animals.
What I really like about my cultural heritage on both sides is the storytelling. The storytelling techniques of each side of the family are totally different, which is why I feel there’s a cultural component. My father’s side of the family told hunting stories with escapades often fueled by alcohol or naivete. Very often the stories started with “Do you remember when …” and end in an absurdity. For example, “Do you remember the time when Ronnie shot the owl up the tree? He ran up to Larry and said, ‘Hey, can you help me get this rabbit out of the tree?’ Larry looked up and saw a dead owl. ‘Ronnie, that’s an owl.’ ‘I wondered how that rabbit got up the tree.'” It’s funnier in person, honestly.
With my mom’s side of the family, the stories often involved word play or other witticisms, and often featured my grandmother as the ‘straight man’ in the joke. My grandmother was confronted with her seventeen-year-old daughter Marie, who said, “I’m going to marry Wayne.” “You can’t marry Wayne,” Grandma said. “Then I’ll elope.” “You can’t elope.” “You watermelon!”
I tell the stories of my family on occasion. I also tell my stories in their ways. One story, as it spread across my peer group, became a friend’s anthropology project in a class. Others can be evoked by their punchlines.
Cultural heritage is a complicated topic in the US, but I can find mine in the stories I have grown up with and the stories I tell.