This is a fairly difficult topic to explain well succinctly (and I’m not that knowledgeable on this topic), but I’ll give it a shot.
To simplify very heavily, light is sorta like an influence that charged particles can have on each other. When a charged particle moves, it induces other charged particles around it to move. But, the influence doesn’t happen instantly, because causality itself isn’t instant, it has to propagate at the speed of causality, aka the speed of light.
Because the electromagnetic field is the field that describes the influence on or by charged particles, this movement influence propagates through the electromagnetic field as a wave (and particle, because of quantization). Thus, it’s an electromagnetic wave, or light.
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