Why wouldn't it be "esta" (with an accent) if we're talking about a cena? That's what I wrote and it told me it was wrong. Since you don't say "this dinner", you need the accent to form a pronoun instead of a demonstrative adjective. And since it's feminine, you need the feminine form.
After minimal investigation, I've come to a usage note on Wiktionary: "The unaccented form can function as a pronoun if there is no ambiguity as to it being a pronoun in its context." But this only explains the accent, not why it uses esto instead of esta. Maybe someone else can enlighten us.
"Esto" is like saying "this situation". For example, when you say "esta comida está bien preparada" [this food is well cooked], you can replace the phrase that makes the situation explicit (esta comida) and put the word "esto" instead to refer to "it" as an implicit situation. The implicit phrase would be "esto está bien preparado". Notice how the gender of the adjective changes since "esto" is a masculine pronoun, which ends up changing the gender of the "it" that is being described.
Everything has a gender in spanish. The only things for which we use neuter words are the abstract concepts such as "the profound [lo profundo], the good [lo bueno], the known [lo conocido], but even then you would still, by intuition, associate them with the masculine gender for the substantive "lo" and for the "o" at the end of those words.
I was going by the following, from http://www.studyspanish.com/lessons/demonstratives.htm
"Each demonstrative pronoun also has a neuter form. They do not change for number or gender, and they are used to refer to abstract ideas, or to an unknown object.
- esto (this matter, this thing)
- eso (that matter, that thing)
- aquello (that matter/thing over there)"