Generally, to give the location of a point you need three coordinates and the moment of time for which these coordinates were valid. To describe the changes of the location (e.g. by plate motion or after earthquakes) you also need a model how the coordinates change with time. E.g., these can be three linear vocities of the point or a plate motion model. Sometimes the point may be regarded as fixed relative to other points, then three coordinates are sufficient. The three coordinates may be cartesian ones (x, y, z), or they may be geographic ones (longitude, latitude, hight), or other types. Sometimes the height is not needed, the two coordinates are sufficient. There are also other methods of defining locations in geomatics, especially when no high accuracy at the m, cm or even mm level is needed, e.g. city names (or zip codes) + street names + house numbers. There are also methods to describe the location of extended areas (cities, lakes, forests, ...) or lines (coastlines, boundary lines, rivers, roads, ...) instead of points, but these are rather methods in geomatics and not in geodesy. The latter mostly deal with points.

A geodetic datum is an abstract coordinate system with a reference surface (such as sea level) that serves to provide known locations to begin surveys and create maps. In this way, datums act similar to starting points when you give someone directions (noaa.gov).

You can see:

https://en.wikipedia.org/wiki/Geodetic_datum

Geodesy deals with the determination of the size and shape of the earth, the external gravity field of the earth and other planetary bodies in time varying space.

The fundamental parameter needed is the geoid model. It provide a basis to ascertain the deflection of the direction of the vertical with that of the normal defining the reference ellipsoid for that location.

Spatial data can be 2D, 3D or 2+1D which ever format the geoid & the reference ellipsoid surfaces becomes critical. This further underscores the need for the geoid model. Further to this, no matter the coordinate system or reference ellipsoid transformation or conversion of coordinates is made seamless with the knowledge of the geoid model within the context of the transformation parameters.

I think the most important parameters that we need to locate a point are the geometrical relationships between the points in a geodetic network. The geometry of a geodetic network makes crucial effects on determining the precision of the coordinates, specially the size of error ellipses. Definition of a datum is also very important in adjustment computations of the network. Without determining the datum parameters, the design matrix will include a rank defect and adjustment computations will be impossible in such a network.