What exactly is current density?

What exactly is the physical significance or meaning of Current density?

The formula $$J=\frac{I}{A}$$ is one thing but what does this represent, I am unable to visualize it or feel it.

We have already defined current as charge flowing through a cross section per unit time as current but now what does current density mean?

For example, while deriving the formula for magnetic field due to a infinite sheet, I came across the term take current per unit area as $$J$$, what information does this give me? I am really confused regarding current density and I don't have any intuitive feeling regarding it. How should I think about it? Please help.

• Related : Surface Current Density. From @Andrew Steane's answer : "Current density" (without any other adjectives) means "charge passing a plane per unit time, per unit area of the plane". "Surface current density" means "amount of charge in a thin sheet of current passing a given place, per unit time, per unit length across the wide dimension of the sheet of current". Sep 4, 2021 at 9:11
• @Frobenius Thanks, understanding it in terms on charge is a bit helpful now. Sep 4, 2021 at 9:19