What exactly are C++ definitions, declarations and assignments?

A definition is where a value or function is described, i.e. the compiler or programmer is told precisely what it is, e.g.

int foo()
{
  return 1;
}

int var; // or, e.g. int var = 5; but this is clearer.

A declaration tells the compiler, or programmer that the function or variable exists. e.g.

int foo();
extern int var;

An assignment is when a variable has its value set, usually with the = operator. e.g.

a = b;
a = foo();

Define and declare are similar but assign is very different.

Here I am declaring (or defining) a variable:

int x;

Here I am assigning a value to that variable:

x = 0;

Here I am doing both in one statement:

int x = 0;

Note

Not all languages support declaration and assignment in one statement:

T-SQL

declare x int;
set x = 0;

Some languages require that you assign a value to a variable upon declaration. This requirement allows the compiler or interpreter of the language to infer a type for the variable:

Python

x = 0

It is important to use the correct terminology, otherwise people will not know what you are talking about, or incorrectly assume that you don't know what you are talking about.