Having immigrant parents gives you a certain set of experiences that only other people in the same boat (no joke intended) would understand. I'm a first generation child, and it's hard to describe exactly what life was like growing up for people whose family is one of generations that have stayed in the one place. When your parents are immigrants, expectations are often different, and the world view is not always the same as those of people who have a strong history or connection to the country they live in. It's hard to describe, because you're not exactly an "other", having been born in your country, but you don't exactly belong, either, having a unique history with the physical place that only just began.
It's not a bad thing. It just is. And it's part of you. It's actually really wonderful in a lot of ways, not in the least because you (hopefully) get to forge a connection to more than one place, or at least get to hear really cool stories from your parents and grandparents. In my experience, it doesn't matter where your parents came from — immigrant values, on a foundational level, are generally pretty similar across the board. (At least in my life, meeting other children of immigrants across all races and nationalities has revealed an overwhelming similarity in the way we were brought up. Maybe these values are the same in local communities too, but I haven't had as much experience with that.) Here are some things only people with immigrant parents will understand:
Immigrant parents generally moved to create a better life for their families, and part of that is getting educated. Growing up, reading and studying were big concerns in my household, and becoming as learned as possible was a preoccupation.
Owning things, whether a business or a property, ties you to a place. It's also symbolic of success. Sometimes, no matter how many career or life achievements you hit, your immigrant parents will still ask, "But when are you going to buy a house?" To wit: I've been saving for property since I was 14.
3. Weird Food
Well, the food isn't weird to you, but it's probably weird to a lot of the kids you grew up with, so at some point you definitely hated it for how it made you stand out. Then you just realized your food is perfectly delicious and wonderful, and probably considered something of a delicacy in the adult world, so you're the best, chuck out the rest.
4. Money Gifts
Immigrant parents don't give presents — they give money, or at least, this is the tradition of every immigrant family I have ever known. And they give it at odd times, like at Easter or for New Years.
5. Not Really Knowing What You Are
A lot of immigrant children have a strange feeling of not quite belonging that ranges from subtle to blatant. For instance, I'm a white person that was bullied by white kids for being Greek. It's a really weird feeling to not experience racism in an institutionalized sense, but to feel like an "other" regardless. I'm not saying "woe is me", and I fully acknowledge that the experiences I had were nothing compared to the prejudice immigrants of color (and non-immigrant people of color) face. But children of immigrants, even if they fully identify as whatever other country their parents emigrated to, sometimes aren't identified that way by the people around them — and it can make for some difficult attitudes to grapple with growing up.