Notice the tie between essentially and the word "essence," referring to the very core of something. As an adverb, then, essentially refers to something's nature. In spite of your faults, you're essentially a good person.
The word essentia came from the Lower Latin, referring to something's inherent qualities. If you're convinced that there's not much difference between two things, you might say that they are essentially the same. Nietzsche once made the essentially sexist comment, "Man wishes woman to be peaceable, but in fact she is essentially warlike, like the cat.”