Here's a quick recap:
A thing's essence is what it is, e.g. a thing's nature. A thing's being is that it is, e.g. a thing's existence.
For example, we can describe a unicorn's essence as a magical horse with a horn. However, that does not mean we are committed to a unicorn's being/existence.
Following Parmenides (although I disagree with him on some implications), I argue that being is one. For, to be distinct from being is to be non-being. Since non-being is literally nothing, anything distinct from being is non-existent. Things can still differ by essence, however, even if they share the same being.
One way of avoiding this conclusion is to postulate that there are different types of being, just as there are different types of essence. The problem with this objection is that distinct entities would therefore be incapable of interacting with one another. If they do not have essence in common, and they do not have being in common, then they have nothing in common. Hence, they have no point of contact in which they are causally related.
I think the unicity of being and the plurality of essence allows us to affirm one of our most fundamental metaphysical beliefs: that existent things are diverse, yet connected.