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The divergence is a crucial tool, for example, in electrodynamics. This can be seen immediately, because the fundamental equations of electrodynamics (called Maxwell equations) contain the divergence of the electric and magnetic fields.
Divergence (div) is “flux density”—the amount of flux entering or leaving a point. Think of it as the rate of flux expansion (positive divergence) or flux contraction (negative divergence). If you measure flux in bananas (and c’mon, who doesn’t?), a positive divergence means your location is a source of bananas. You’ve hit the Donkey Kong jackpot.
Vector Calculus: Understanding Divergence by Kalid Azad