The issue in Butler regarded when an accused person is deemed to have waived his (Butler was male) right against self-incrimination.
Butler was arrested and was read his rights. He made a verbal statement indicating that he understood his rights. He refused to sign a form saying that he was waiving those rights. However, he still went ahead and answered questions and incrimnated himself. He never tried to stop the questioning and never requested a lawyer.
The Supreme Court ruled that Butler's verbal statement was sufficient evidence that he understood his rights. Therefore, when he answered questions and made statements, he was doing so voluntarily and with full knowledge of his rights. Therefore, his inculpatory statements were admissable as evidence.