How can polymorphism be described in an easy-to-understand way?
We can find a lot of information about the subject on the Internet and books, like in Type polymorphism. But let's try to make it as simple as we can.
Polymorphism is the storing of values of more than one type in a location of a single type.
Note that most of the other answers to this question, at the time of my writing, are actually describing dynamic dispatch, not polymorphism.
Dynamic dispatch requires polymorphism, but the reverse is not true. One could imagine a language very similar to Java or C# but whose System.Object had no members; typecasting would be necessary before doing anything with the value. In this notional language, there would be polymorphism, but not necessarily virtual methods, or any other dynamic dispatch mechanisms.
Dynamic dispatch is the related but distinct concept, well enough described in most of the other answers. However, the way it normally works in object-oriented languages (selecting a function based on the first ('this' or 'Self') argument type) is not the only way it can work. Multiple dispatch is also possible, where the selection is applied across the types of all the arguments.
Similarly, overload resolution and multiple dispatch are exact analogues of one another; overload resolution is multiple dispatch applied to static types, while multiple dispatch is overload resolution applied to runtime types stored in polymorphic locations.