What does Luke 1:62 mean?

The father mentioned here is Zechariah (Luke 1:5–7). When Zechariah doubted the words of an angel who predicted he'd become a father (Luke 1:13–18), he was stricken speechless (Luke 1:19–20). When the baby was finally born (Luke 1:57) and ready to be named (Luke 1:59), those supervising the ceremony plan to name the baby after Zechariah. Elizabeth, the mother, insists that the child be named "John" (Luke 1:60), to the confusion of their family (Luke 1:61).

It seems likely—or at least possible—that Zechariah was also rendered deaf by his encounter with the angel. Such a condition would fit the nature of his rebuke. He rejected the angel's words, so he would be unable to speak words of his own. He rejected what he heard, so he would be unable to hear other speech. That people communicate with him by making signs suggests that talking to him would not work.

While Zechariah cannot speak, he can write (Luke 1:63). What he indicates is exactly what Elizabeth wanted, and is what Gabriel commanded (Luke 1:13). This fulfills the term of his punishment, allowing him to speak, and amazing those who see these things happen (Luke 1:64–65).