I supported myself on unemployment without living with my parents. How and why do I fill out form 8615?

Form 8615, Tax for Certain Children Who Have Unearned Income, is required when a child meets all of the following conditions:

1. The child had more than $2,200 of unearned income (which includes unemployment compensation).
2. The child is required to file a tax return.
3. The child either:
   1. Was under age 18 at the end of 2020,
   2. Was age 18 at the end of 2020 and didn’t have earned income that was more than half of the child's support, or
   3. Was a full-time student at least age 19 and under age 24 at the end of 2020 and didn’t have earned income that was more than half of the child's support.
4. At least one of the child's parents was alive at the end of 2020.
5. The child doesn’t file a joint return for 2020.

Per the IRS, if your parent's taxable income, filing status, or net unearned income of your parent's other children isn't known by the due date of your return, reasonable estimates can be used.

If you use estimated amounts, you have to write “Estimated” next to the appropriate line(s) of Form 8615. Please keep in mind that you will have to mail in your tax return and will not be able to e-file if you are required to make written notations on your return. When the correct information becomes available, you can file Form 1040-X, Amended U.S. Individual Income Tax Return.

Although kiddie tax applies whether or not you are a dependent of your parents, it does not seem like you would be a dependent from your question.  

Your parents would only be able to claim you as a dependent under the qualifying child rules if all of the following requirements are met:

• You aren't claimed as a dependent by someone else.
• You're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• You aren’t filing a joint return with your spouse.
• You're under the age of 19 (or 24 for full-time students).
  • No age limit for permanently and totally disabled children.
• You lived with them for more than half the year (exceptions apply - such as: away at college).
• You didn't provide more than half of your own support for the year.