Drupal - How do I access field data in Twig?

content contains the render arrays based on the configured formatters.

If you want to access the actual values, you want to access them through the entity object. Usually, that is available already to your template, for example node. For your case, it is a bit special because the block_content is rendered in the block content without its own template, so you have to make it available yourself in a yourtheme_preprocess_block($variables) like this:

if (isset($variables['elements']['content']['#block_content'])) {
  $variables['block_content'] = $variables['elements']['content']['#block_content'];
}

Then, you can access a field value with block_content.field_name.property. So in your case, block_content.field_align.value. The property is value for most field types, for references, you can either use target_id for the ID or entity for the referenced entity object. Yes, you can directly access fields on that, but make sure to always check that a reference exists otherwise you can end up with fatal errors or exceptions. To access the label of a term reference for example, you can access it as block_content.field_tags.entity.name.value.

If you don't specify the field delta, it defaults to the first. If you want to access a different delta, you can use entity.field_name.1.valueand so on. You can also loop over them.

This all maps directly to PHP, you can also do $block_content->field_tags->entity->name->value in preprocess and other places where you have the block_content.

Here's an alternative, template only way which allows you to render a render array and check its value (allows checking the variable as if you were printing it, because printing in Drupal 8 Twig automatically renders variables that are render arrays):

{{ kint(content.field_align|render == 'right') }}

Or another option to save the extra render if you're printing the variable later:

{% set field_align = content.field_align|render %}
{{ kint(field_align == 'right') }}

{{ field_align }}

You can use Twig Field Value module in this case. It allows to get partial data from field render arrays. For ex. content.field_name|field_value -get value of field. You can use it in IF statement