The original use case for Surface Classifications was for Volume Calculations.
In most software - when you compute volumes between Surface 1 and Surface 2 you will get a Cut and Fill number. If you get the surfaces the wrong way round, the Cut and Fill numbers will reverse. This is because the software does not know anything about the date or time when the surface was actually there or where it is intended to be in the date time hierarchy for a project. By naming surfaces in a good way you can more reliably pick the correct order - but again if you get the order wrong then you will get Cut and Fill the wrong way round and on a report that you hand off to someone else to read, they are even less likely to know whether the numbers are right or wrong.
So in TBC we created a Hierarchy where surfaces can be classified into eg
Original Ground
Strata
Work In Progress
Design
Subgrade
Overexcavation
Stockpile
Depression Volume
And in addition surfaces can be given a Creation date as well
If you compute a volume between surfaces classified as Original Ground and Design, or if you switch them and do Design and Original Ground, the classification helps TBC decide which way around to compute the volumes between the surfaces - they will always be computed Original - Design.
If you classify a Work In Progress Surface then the hierarchy is Original then Work In Progress and then Design for the volume calculations.
In addition to all of this, some surface settings are changed for an Original Ground and for a Design Surface as was outlined in the post that Matthew Judice referenced a while back, to handle different scenarios that are encountered in Design surfaces vs typical Original Ground surfaces.
The Date and Time also adds another level of hierarchy to separate two surfaces of the same type - e.g. two Work In progress Surfaces measured at different dates and times.
I hope that this helps to explain the system.
Alan