Binary shows each byte as its eight individual bits. It is more verbose than hex and occasionally more useful, because some values are not numbers at all — they are collections of independent flags packed into a single integer, and only the bit view makes that legible.
When it helps
Whenever a value is a bitmask rather than a quantity. Unix file permissions, feature flags packed into a column, protocol header fields, network masks: in all of them a change from one number to another is meaningless until you see which bits moved. Reading a permission value as a decimal number tells you nothing; reading it as bits tells you exactly which capability was granted or removed, which is usually the question.
Worth running automatically
The conversion is a one-off, but the values it explains are worth watching. A flags field that changes represents a configuration change, and where those values are exposed by an endpoint, monitoring the response content catches the change even though the status code never varies. That is the general pattern: the conversion helps you read it once, and content-level checking notices when it moves.
What you get out of it
The only readable view of a value that is really several independent switches. It turns an opaque integer into a specific statement about which flags are set.