Many Joomla! sites are structured as magazines where authors publish articles about new products, services or whatever other stuff. In this type of website, readers may get interested by article's topics and would appreciate an easy way to ask for additional info about the topic covered in the article.
Supposed it´s a catalog site, the potential customer (web user) would like to contact directly the article author (the seller) to ask him/her for additional information, price or any other data. Doing so just by a mouse click (on a form) would be ideal.
That´s what Inforequest is supossed to do. Generalizing, any website where readers may wish to contact article authors is suitable for this extension.