Smart quotes really refers the feature some software has where it automatically detects what type of quote should be used (opening or closing) and puts that in so you can just use the same quote key at the beginning and end and it'll substitute in the right "smart quote".
They are smart because the feature that inserts them is "smart". "Context-aware quotes" or "smartly inserted quotes" might be more accurate.
A PM somewhere probably thought "smart quotes" sounded neat, and here we are.
Because option to enable substitution of minutes(') and seconds(") symbols by proper quotation marks is often called as «Enable smart quotes».
For example: 10° 33' 19" -> 10° 33« 19». Very smart!
Good post! I must point out, though, the correct symbol for minutes and seconds is actually the prime. As in, 10° 33′ 19″.