What is IdentityInterface in Magento2

From what I understood, this is kind of the equivalence of the getCacheTags method of Magento 1.

The getIdentities from model classes is then used in every block class referencing this model.

Ok let's take the /Magento/Catalog/Model/Category.php:

public function getIdentities()
{
    $identities = [
        self::CACHE_TAG . '_' . $this->getId(),
    ];
    if ($this->hasDataChanges() || $this->isDeleted()) {
        $identities[] = Product::CACHE_PRODUCT_CATEGORY_TAG . '_' . $this->getId();
    }
    return $identities;
}

This method is then referenced in /Magento/Catalog/Block/Category/View.php:

public function getIdentities()
{
    return $this->getCurrentCategory()->getIdentities();
}

In M2, you now have to declare the cache tag with the getIdentities method at the model level, then you can use it in blocks referencing those models.

If you check every block implementing the getIdentities method, they all reference a corresponding model getIdentities method or a corresponding model cache tag such as \Magento\Catalog\Model\Product::CACHE_TAG

Then those block getIdentities methods are used in Varnish for caching reasons as mentioned by Matthéo to set the X-Magento-Tags header.

This header is then used in Magento/Framework/App/PageCache/Kernel.php in the process() method to save the cache:

$tagsHeader = $response->getHeader('X-Magento-Tags');
$tags = $tagsHeader ? explode(',', $tagsHeader->getFieldValue()) : [];

$response->clearHeader('Set-Cookie');
$response->clearHeader('X-Magento-Tags');
if (!headers_sent()) {
    header_remove('Set-Cookie');
}
$this->cache->save(serialize($response), $this->identifier->getValue(), $tags, $maxAge);

Judging by the class Magento\Framework\DataObject\IdentityInterface comment it is used for cache and make a unique entity ID that is used in Varnish ESI headers in vendor/magento/module-page-cache/Controller/Block/Esi.phpline 28.

if ($blockInstance instanceof \Magento\Framework\DataObject\IdentityInterface) {
   $response->setHeader('X-Magento-Tags', implode(',', $blockInstance->getIdentities()));
}

The  IdentityInterface  will  force  Model  class  to  define  the  ​getIdentities()  method which  will return a unique id for the model. You must only use this interface if your model required cache refresh after database operation and render information to the frontend page.