Introspection means that the program's structures and procedures are discoverable and we can query about them. Typical questions we might want to have answers for:
* find me the class, typically by name or by some relationship
* what are the fields of that class?
* find me a function
* what are the arguments of the function? does it have documentation? Who wrote it? Where is its source? What values does it return?
* where is the function used? what functions does it call?
* what are the values of a field of some object? What class does it have?
This and more for example enables you to inspect a program at runtime and find out what it does, how it does it and what its state currently is.
Reflection means that elements of the programming language are itself exposed and we can change/extend them.
Two examples of the Lisp world. Very unusual is the reflective tower, where a Lisp program is run by some kind of machine, which for example is a Lisp interpreter. This Lisp interpreter is itself a Lisp program. Thus you can not only write the program, but you can change/extend the interpreter running the program. A certain Lisp dialect allowed also to look at the interpreter running the interpreter running the interpreter running the interpreter ...
In Common Lisp a typical form of reflection is the Meta-Object Protocol of CLOS. It allows you to program the object system to implement new variants: persistent objects, transactions over objects, different inheritance mechanisms, classes which record their instances, ... Thus the MOP exposes classes, methods, generic functions, slot descriptors, ... as CLOS classes and methods - and protocols about them. Thus CLOS can be programmed in itself. Even at runtime.
More primitive reflection would allow you to create/change/remove things like user classes and user methods. Task: create a new subclass of an existing class at runtime.