What happens to my annual leave days if I resign?

Vacation days that you have earned but not taken are paid as vacation pay on your final salary. So you get money instead of time off.
Your employer cannot force you to take vacation during your notice period if your notice period is less than 6 months. In this case, it is up to you to decide whether you want to apply for vacation or not.
There are different ways of accruing and taking annual leave. When holiday is earned and when it can be taken is regulated by collective agreements or the Annual Holidays Act. Advance holiday is sometimes taken in connection with new employment. If you resign, you usually have to "pay it back" by offsetting it against your holiday pay. Ask your employer if you are unsure whether you have a vacation debt from advance vacation that needs to be paid back.