The following article is an excerpt from this book.

Generally speaking, to be earnest means to be sincere and serious.  When one prays with earnestness, he prays showing deep sincerity or seriousness; thus, he is determined, fervent and intense in his prayers.  And we could say that the reason one prays with such seriousness is because he finds that the need is so great and that prayer is so important, that it is the only way to find the answer or to satisfy the need.

Now when you have a longing, a craving, and a yearning to satisfy a need, that is the desire of prayer.  It is what God puts in you.  But if you want that desire to be fulfilled you must follow up that desire by praying with earnestness.  For when you pray with earnestness, what you are doing is you are putting that desire to work…