What is static and dynamic type checking?

Static type checking, sometimes known as static typing, is when the compiler checks the type correctness of operations at compile time. For example, the compiler checks the parameter types of function arguments and checks that a member function invocation is guaranteed to work at runtime, then it flags improper matches as errors at compile time. For example, if class X has member function f() but not member function g() and x is an instance of class X, then x.f() is legal and x.g() is illegal.
Dynamic type checking, sometimes known as dynamic typing, is the determination of type correctness at runtime. With dynamic type checking, user code determines whether an object supports a particular member function at runtime rather than at compile time. Dynamic type checking is often accompanied by downcasts and can unnecessarily increase the cost of C++ software. Runtime type identification (RTTI) is one kind of dynamic type checking that is supported directly by C++.