What does "from the bottom of one's heart" mean?

Most sincerely, unreservedly. For example, I want to thank all of my supporters from the bottom of my heart, or She wished, from the bottom of her heart, that her daughter would get well. In English this term appeared in the Anglican Book of Common Prayer's Communion service (1545): “If one ... be content to forgive from the bottom of his heart”; in Latin it dates back to Virgil.