{% set monthIds = craft.categories.group('months').ids() %}

{% for monthId in monthIds %}
    <div>
        {# group each months entries #}
        {% for item in craft.entries.section('sectionName').relatedTo({targetElement:monthId}) %}
            {# content for each entry. #}
        {% endfor %}
    </div>
{% endfor %}

{# 1 == January #}

{% for month in 1..12 %}
    <div>
        <h2>MONTH {{ month }}</h2>
        {# group each months entries #}
        {% for item in craft.entries.section('blog') if item.postDate|date("n") == month %}
            {# content for each entry. #}
            <h3>{{item.title}}</h3>
        {% endfor %}
    </div>
{% endfor %}