A ‘reinclusion request’ is a formality for making a reconsideration request to Google, or other search property, to be re-indexed after having been penalized by the search property for engaging in practices, wittingly or not, that go against its policies for inclusion.
There are many reasons your web pages may have dropped in rank or been excluded altogether from the search engine. If you suspect your website is being penalized it is in your best interests to hire a reputable SEO firm immediately to analyze and resolve the issues that caused the problems.
Once the problems have been addressed satisfactorily, your SEO professional will make a formal ‘reconsideration request’ to Google, or other search property, demonstrating the fixes that were made that have brought the website into compliance.