Maxwell's equations combined the famous results from Electricity and Magnetism (and throw in an extra result needed to balance things out) and by expressing these in vector calculus revealed that a an electromagnetic wave form, (of which light is just one example), would have to travel at a speed given by certain constants which turned out to be the same as the speed of light. This result led to an amazing range of discoveries about electromagnetic radiation of all kinds.
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Not everything can be made simple; but it is great that you are interested.
Here are some basics. A better understanding might require college level familiarity with vector calculus and perhaps some physics as well and some time spent applying this to specific examples.
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Del Operator: Used in both alternative forms of div and curl below. Defined as
Del = (∂/∂x)i + (∂/∂y)j + (∂/∂z)K
We treat it as if it were a function and when writing it out the vector, (V say), that it operates on gets inserted in from of each partial derivative like this:-
Del V = (∂V/∂x)i + (∂V/∂y)j + (∂V/∂z)K (the gradient vector)
Note: The del symbol, (does not post well) is a small triangle pointing downwards.
Also see this web page.
http://users.aber.ac.uk/ruw/teach/260/del.php
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Divergence: (a vector operator)
When considering the velocity field of a flowing fluid or other quantity the physical interpretation of divergence is the net rate of change of the mass of the fluid flowing from a given point per unit volume. It is a measure of the tendency of a fluid to diverge from that point, and as such measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar.
If div F is zero then the fluid is called incompressible.
If the vector field F = Pi + Qj + Rk, (where i, j, k are unit vectors)
Div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z
It can also be expressed as del . F, (del dot product vector field F)
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Curl: (a vector operator)
The physical significance of the curl of a vector field is the amount of "rotation" or angular momentum of the contents of given region of space. It arises in fluid mechanics and elasticity theory. It is also fundamental in the theory of electromagnetism, where it arises in two of the four Maxwell equations. If curl F is zero then the fluid is called irrotational.
If the vector field F = Pi + Qj + Rk, (where i, j, k are unit vectors)
Curl F = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)j
It can also be expressed as del X F, (del cross product vector field F)
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This website has some images of sources sinks and rotational flow
http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/guidedtour/Tour.htm
Regards - Ian