What is the difference between a definition and a declaration?

From the C++ standard section 3.1:

A declaration introduces names into a translation unit or redeclares names introduced by previous declarations. A declaration specifies the interpretation and attributes of these names.

The next paragraph states (emphasis mine) that a declaration is a definition unless...

... it declares a function without specifying the function’s body:

void sqrt(double);  // declares sqrt

... it declares a static member within a class definition:

struct X
{
    int a;         // defines a
    static int b;  // declares b
};

... it declares a class name:

class Y;

... it contains the extern keyword without an initializer or function body:

extern const int i = 0;  // defines i
extern int j;  // declares j
extern "C"
{
    void foo();  // declares foo
}

... or is a typedef or using statement.

typedef long LONG_32;  // declares LONG_32
using namespace std;   // declares std

Now for the big reason why it's important to understand the difference between a declaration and definition: the One Definition Rule. From section 3.2.1 of the C++ standard:

No translation unit shall contain more than one definition of any variable, function, class type, enumeration type, or template.

There are interesting edge cases in C++ (some of them in C too). Consider

T t;

That can be a definition or a declaration, depending on what type T is:

typedef void T();
T t; // declaration of function "t"

struct X { 
  T t; // declaration of function "t".
};

typedef int T;
T t; // definition of object "t".

In C++, when using templates, there is another edge case.

template <typename T>
struct X { 
  static int member; // declaration
};

template<typename T>
int X<T>::member; // definition

template<>
int X<bool>::member; // declaration!

The last declaration was not a definition. It's the declaration of an explicit specialization of the static member of X<bool>. It tells the compiler: "If it comes to instantiating X<bool>::member, then don't instantiate the definition of the member from the primary template, but use the definition found elsewhere". To make it a definition, you have to supply an initializer

template<>
int X<bool>::member = 1; // definition, belongs into a .cpp file.

A declaration introduces an identifier and describes its type, be it a type, object, or function. A declaration is what the compiler needs to accept references to that identifier. These are declarations:

extern int bar;
extern int g(int, int);
double f(int, double); // extern can be omitted for function declarations
class foo; // no extern allowed for type declarations

A definition actually instantiates/implements this identifier. It's what the linker needs in order to link references to those entities. These are definitions corresponding to the above declarations:

int bar;
int g(int lhs, int rhs) {return lhs*rhs;}
double f(int i, double d) {return i+d;}
class foo {};

A definition can be used in the place of a declaration.

An identifier can be declared as often as you want. Thus, the following is legal in C and C++:

double f(int, double);
double f(int, double);
extern double f(int, double); // the same as the two above
extern double f(int, double);

However, it must be defined exactly once. If you forget to define something that's been declared and referenced somewhere, then the linker doesn't know what to link references to and complains about a missing symbols. If you define something more than once, then the linker doesn't know which of the definitions to link references to and complains about duplicated symbols.

---

Since the debate what is a class declaration vs. a class definition in C++ keeps coming up (in answers and comments to other questions) , I'll paste a quote from the C++ standard here.
At 3.1/2, C++03 says:

A declaration is a definition unless it [...] is a class name declaration [...].

3.1/3 then gives a few examples. Amongst them:

[Example: [...]
struct S { int a; int b; }; // defines S, S::a, and S::b [...]
struct S; // declares S
—end example

To sum it up: The C++ standard considers struct x; to be a declaration and struct x {}; a definition. (In other words, "forward declaration" a misnomer, since there are no other forms of class declarations in C++.)

Thanks to litb (Johannes Schaub) who dug out the actual chapter and verse in one of his answers.

Declaration: "Somewhere, there exists a foo."

Definition: "...and here it is!"