Trouble with Twig `embed` tag
I'm going to assume that, as per the use cases in the documentation, embed is a good fit for your requirements.

If you're not sure, extends and include are probably a better choice, as they're much easier to understand and work with.

Moving on, in your example you appear to have confused the roles of the template being embedded, and the template doing the embedding.

Here's how it should look:

{# Page (doing the embedding) #}
{% embed "_partials/sidebar" %}
    {% block subscribe %}
        The custom subscribe block content.
    {% endblock %}
{% endembed %}

{# Embed (being embedded) #}
&lt;div class="sidebar"&gt;
    &lt;div class="sidebar__subscribe"&gt;
        {% block subscribe %}
            The (optional) default subscribe block content.
        {% endblock %}
    &lt;/div&gt;
&lt;/div&gt;