Explain the Ontological Argument

The Ontological argument is an a-priori argument (without any experiential evidence - pure logic - analytical & deductive) to establish the existence of God. It also follows 'de dicto' logic; that by definition, the conclusion can be reached.
There are two famous postulations of the Ontological Argument that both prove the existence of God. The first is put forward by Anselm in the 11th Century in Proslogium. He states that God can be defined as a being 'than that which nothing greater can be conceived,' (TTWNGCBC) Thus, by understanding this definition, we must also believe in the existence of God (de dicto proof). Secondly, if we conceive of this in our mind (in intellectu), then by definition, we must conceive of this in reality, (in re). Let us use his painter analogy to understand this: he states that a painter can conceive of the greatest painting in his mind, but for it to be the greatest painting, it must exist in reality. That is the same with the principle of God. For if we understand the first premise of TTWNGCBC then we can postulate that he is only the 'greatest' in reality (like the painting), thus God must exist.
Descartes also puts forward his version of the ontological argument. He states cognito ergo sum (I think, therefore I exist.) Then, he states he is an imperfect being with a concept of a perfect being (God). Thus a perfect being must have existed to place this concept of a 'perfect being' in his mind. Thus, following Anselm's definition, this perfect being must be God. Further echoing Anselm, he states that existence is a perfection, and since by definition God has all 'perfections', he thus, must exist.