Getting Matrix content from within a relationship field
Twig is quite different from the EE parser – much more in line with how PHP is interpreted (Twig actually compiles to PHP before rendering).

First, the use of gallery in your for loop is arbitrary – its just the name you pick for the variable containing the currently iterated item, and its completely up to you. So this would work just as well:

{% for galleryEntry in block.galleryInclude %}
    {{ galleryEntry.title }}
    ...
{% endfor %}


Second, there are a couple of issues with your code. For one, you'll need to use another for loop to access the slides inside the galleryMatrix field. Note that you can use "block" as the variable name here as well (unless you need to access any of the outer block variable's properties), but let's call it "slide" for clarity:

{% for slide in gallery.galleryMatrix %}
    ...
{% endfor %}


Note that if your galleryMatrix field contains multiple block types and you're only interested in the "slide" block type, you can for test the slide.type property inside the loop, or use the type method to filter the galleryMatrix field:

{% for slide in gallery.galleryMatrix.type('slide') %}
    ...
{% endfor %}


Furthermore – this is a common gotcha for new Craft users – even if there's only 1 asset, you'll always need to loop through any Asset field; you can't just put assetField.getUrl(). So, you'll need another loop to pull your slide image(s) inside the galleryMatrix loop:

{% for image in slide.slideImage %}
    &lt;div&gt;&lt;img src="{{ image.getUrl() }}" /&gt;&lt;/div&gt;
{% endfor %}


Sidenote; when there's only a single asset you could also do the following, but as you'll need an if statement the amount of code won't be any less:

{% set slideImage = slide.slideImage.first() %}
{% if slideImage %}
    &lt;div&gt;&lt;img src="{{ asset.getUrl() }}" /&gt;&lt;/div&gt;
{% endif %}


Putting it together, here's what your full code should look like (not tested, but should work based on the info you gave):

{% for gallery in block.galleryInclude %}
    {{ gallery.title }}

    &lt;figure&gt;
        {% for slide in gallery.galleryMatrix %}
            {% for image in slide.slideImage %}
                &lt;div&gt;&lt;img src="{{ image.getUrl() }}" /&gt;&lt;/div&gt;
            {% endfor %}
        {% endfor %}
   &lt;/figure&gt;

{% endfor %}