The number of dimensions depend on what it relates to.
With a (hypothetical) zero-size point, the dimensions are it's location in space or from whatever the zero reference is for your coordinates (along the axes you are using), not size.
eg. An endpoint of a line, or corner of a square or cube.
You can define that point by coordinates in two dimensions or three dimensions (depending if it's a flat drawing or 3D model) to show its location, but in themself those coordinates are nothing to do with size.
Or points on a graph; no size, just coordinates.
Or, "A point in time" - no duration, just a reference that can be used as an endpoint of a duration (like clicking a stopwatch to start or stop it).
Add other points in the same coordinate system and you can measure/define distance or duration between them.