When your account is past its due date, it means the minimum payment required was not paid on time.
A missed payment on your credit card statement will show as "past due date" after the last payment due date.
You can now expect a late fee to be added to your charge, in addition to the interest charged on the carry over balance.
If you continue to miss paying your minimum balance, increased credit charges will be added to your account.
If you can pay within 30 days, you could still save the missed payment from impacting your credit score.
If you're over 180 days or 6 months late, your account may be closed. You'll have no choice but to pay the balance in full.
Your credit card agency may also assign your account to a collection agency who can hound you to pay.
This can negatively affect your ability to make purchases as well as impacts your budget with high interest rates.
Your credit score will take a hit. The next time you apply for a loan or credit card, you could be denied.