I am assuming the phrase is used in relation to a legal claim, in which case it means to withdraw the claim without the right to refile it at a later time.
This is contrasted with "withdraw without prejudice" which would, obviously, mean that the right to refile the claim remains.
Without prejuedice means that the decision is not irrevocable. That, in this instance, at some time in future you may withdraw the notice to quit.
It can, but not always. Withdraw can also mean take.
withdraw to take out like a negative
When someone says that prejudice prevails they mean that prejudice has won. This means that justice was not found for example.
to take away
Separate yourself from it
Rescind
To extract, take out, withdraw
To extract, take out, withdraw
Then you are being prejudice.
Prejudice
antipathy, intolerance