What does "finished" mean?

1. (completed) having come to an end or being completed. 2. (refined or polished) made to look perfect or high-quality through careful work. 3. (doomed or exhausted) having no more power, money, or chance of success.

Is it correct to say "I am finished my homework."?

No — say "I have finished my homework.". When 'finished' is the main action, use 'have'. Use 'am finished' only as an adjective to describe your state of being done.

finished

adj.

US //ˈfɪnɪʃt// UK //fˈɪnɪʃt// fin·ished

1 completed (adj.)
A2 Elementary

having come to an end or being completed.

having reached an end; concluded or brought to a state of completion.

Example

Are you finished with that book yet, or do you need more time?

Example

Once the report is finished and proofread, please submit it to the department head for final approval.
Pitfall

I am finished my homework.

I have finished my homework.

When 'finished' is the main action, use 'have'. Use 'am finished' only as an adjective to describe your state of being done.
2 refined or polished (adj.)
B2 Upper Intermediate

made to look perfect or high-quality through careful work.

brought to a highly polished or perfected state; often used regarding materials or artistic performances.

Example

The finished wood on the table was smooth and shiny.

Example

The pianist gave a very finished performance, showing technical mastery and deep emotional maturity.
- rough
- raw

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3 doomed or exhausted (adj.)
B2 Upper Intermediate Informal

having no more power, money, or chance of success.

experiencing a total loss of resources, power, or viability; figuratively doomed.

Example

If we don't find more water soon, we are finished.

Example

After the scandal went public, the politician knew his career was effectively finished.