1. What does it mean?
비번 is the everyday abbreviation of 비밀번호. It can refer to a login password, a device passcode, or the code for a permitted shared service such as guest Wi-Fi.
Also written or said as 비밀번호, bibeon
2. The nuance
It does not only mean a number, despite 번호 in the full word. The abbreviation also has unrelated dictionary meanings; the account or access context identifies this one.
3. Examples
“카페 와이파이 비번은 영수증에 적혀 있대.”
They say the cafe's Wi-Fi password is printed on the receipt.
“비번을 잊어서 계정 복구 절차를 확인했어.”
I forgot my password, so I checked the account-recovery steps.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.