Var doesn't let you, the programmer, declare a variable because Javascript doesn't have variables. Javascript has objects. Var declares a name to an undefined object, explicitly. Assignment assigns a name as a handle to an object that has been given a value.
Using var tells the Javacript interpreter two things:
Omission of var tells the Javacript interpreter to use the first-found previous instance of an object with the same name.
Var as a keyword arose from a poor decision by the language designer much in the same way that Javascript as a name arose from a poor decision.
ps. Study the code examples above.