Greek philosophy, not Celtic religion
Earth, air, fire and water as a set of four come from classical Greek philosophy (Empedocles and later Aristotle) and reached modern Wicca through medieval and Renaissance ceremonial magic, and then through groups like the Hermetic Order of the Golden Dawn. They are not a documented ancient Celtic system.
How Wiccans generally use them
Many Wiccan rituals assign an element to each of the four compass directions, often with a fifth (spirit, or aether) at the centre. Which element sits in which direction varies between traditions and, sensibly, between landscapes.
In plain English
The elements are a set of shorthand categories for qualities: solidity, thought, energy, feeling. They are a way of organising attention, not a claim about chemistry.