As it was explained to me, dhatu means something like "aspect" or "tier". Meaning, it's a cross-cutting principle found in a whole that's delineated when you analytically disect the whole in a particular way.
So, when you analyze experience, you may delineate "the visual aspect" - present across many rather different experiences. When you analyze external dharmas, you may delineate "the aspect of solidity" present across many very different objects etc.
Today we could delineate e.g. the electromagnetic aspect, the chemical aspect, the informational aspect. All are elements or principles of the whole observed as different "analytical planes".
ChrisW is not wrong to explain it as he did for the purpose of contrasting dhatu with the chemical elements of the periodic table. They are subjective inasmuch as it takes an act of analysis to delineate and "focus" on one dhatu at a time. Of course they are also objective because they are actual aspects of an ontological whole.
As part of the gradual instruction, Buddha taught basic phenomenological analysis, delineating dhatus such as "the seen", "the heard" etc.
The culmination of his teaching, though, is the notion of amrita-dhatu aka dharmadhatu, the most fundamental aspect of everything. Seeing this dhatu is seeing Nirvana. This dhatu can be described as the absolute reference point, substratum of all fluctuation.