Where are you? I'm getting the impression (despite the use of "gotten", which is a thoroughly American word) that you're British. So I will answer from that point of view.
It's not really bad. After all, you can't even HAVE a current account until you're 18 for legal reasons. And there are plenty of older people just as incompetent (unfortunately). But now is a great time to learn! The best part is that you're thinking about this and asking.
At 17, any account you already have will be the kind where you can't have an overdraft. Banks just won't let under 18s have an overdraft because it means borrowing and they're not going to let you do that if you're not a legal adult. They can't sue you to get the borrowed money back if you're not a legal adult. Of course they won't do that unless you keep on not paying, but they want to have that power as a last resort if they have to. Which is why you can't have a current account (which a student account also is - it's a current account with student perks) until 18.
If you have one of those, it's possible to go into overdraft by taking out more than you actually have, or writing a cheque for more than you have. In that case, the amount in your account goes negative - you have an overdraft - and the bank will charge fees and interest until the account goes positive again. It can be handy to go into overdraft for a bit until you get some more money, and it's the cheapest way to borrow for a short period, but you really don't want to do it too often.
You have a card... at 17 this will be a debit card. Credit cards mean borrowing and you can't do that until 18. You MUST have a bank account because a debit card is only a way of using it. How do you put money on the card so you can use the card to spend? That's depositing money into the account, so you already know how to do it! I bet this is why the lady asked what account you already have - you must have one so you can have the card.
I've found this with a lot of young people - they want a debit card, and don't realise it's only an appendage to the account that you must have so the bank can give you the card that goes with it.
Then what if you have spare money? You could put that into a savings account. No card, no overdraft, you can just deposit money and take it out, but you get interest. Literally, the bank gives you free money just for leaving your money with them. These days it's not much, but it's a little something.
That's about as much as you need to know for now!