They are equations that relate functions to their derivatives. Which isn’t much help unless you have an idea what that means already…. but basically they are equations which consider the rates of change between different variables and how to get a meaningful answer out of a system with several variables if you have these rates of change for the variables as they relate to one another.
So if you can get past my mealy-mouthed explanation, the takeaway here is that they are an incredibly powerful way of describing (sometimes approximately, especially when you get to more complex systems) how much stuff will do what, at what sort of rate.
This is vital to physics, but also has extremely wide applications in pretty much all the sciences.
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