What do we think this term means? I.e. what quantity, or what sort of quantity, does it signify?

The question is ambiguous, depends on the observer.

Since no one knows what you are trying to get at it helps to elaborate.

The only thing I can guess at it is: what's the engineering units of [$]\sqrt{T - t}[$]. ? [$]d_1[$] should be dimensionless.

Or a number in a formula.

T is the time at expiry, t is the time at which the option is priced. Therefore T-t is the time to expiry. Units would be seconds, hours, or whatever unit of time is chosen. The square root of that is the number which, multiplied by itself, equals T-t.

"Since no one knows what you are trying to get at ...". It should be clear what I am trying to get at, namely what the term means. Time to expiry seems clear. What about sigma? I searched in Hull this afternoon and could find no clear answer. He introduces the term 'volatility' without explaining at any place exactly what he means.