Why does my JavaScript get a “No 'Access-Control-Allow-Origin' header is present on the requested resource” error when Postman does not?

I am trying to do authorization using JavaScript by connecting to the RESTful API built in Flask. However, when I make the request, I get the following error:

XMLHttpRequest cannot load http://myApiUrl/login. No 'Access-Control-Allow-Origin' header is present on the requested resource. Origin 'null' is therefore not allowed access.

I know that the API or remote resource must set the header, but why did it work when I made the request via the Chrome extension Postman?

This is the request code:

$.ajax({
    type: "POST",
    dataType: 'text',
    url: api,
    username: 'user',
    password: 'pass',
    crossDomain : true,
    xhrFields: {
        withCredentials: true
    }
})
    .done(function( data ) {
        console.log("done");
    })
    .fail( function(xhr, textStatus, errorThrown) {
        alert(xhr.responseText);
        alert(textStatus);
    });

#postman