Great question.
Contemporaries of Descartes had noted that "I think, therefore I am (or I exist)" looked like something that Augustine had forwarded several centuries earlier. So, they wondered why Descartes was treating it as though he had come up with something new. And, others complained that Descartes had muddied things by not laying out the entire argument -- which, they claimed, should've looked something like this:

1. Everything that acts exists.
2. Thinking is an act.
3. I am thinking.
4. Therefore, I exist.

Descartes said to the one group of critics that he was not aware of Augustine's having made the claim (some scholars have wondered whether he was telling the truth here), and to the other group that he had not intended the phrase to express an argument -- despite the fact that it sported the conclusion indicator term "therefore". The phrase wasn't expressing a movement of the mind, from premises to conclusion. Instead, he claimed, the phrase was supposed to express something that immediately struck the mind as completely and utterly true, a kind of A HA! moment -- namely, that when one considers the fact that he or she is thinking, one cannot but be immediately struck by the insight that he or she exists (while doing the considering). So, one has the immediate insight that one exists while one thinks; one doesn't come to this by way of an argument.

Scholars have referred to this phrase -- "I think, therefore I am" -- as "the cogito" ("cogito" in Latin means "I think" or "I am thinking"). As Finnish philosopher Jaakko Hintikka famously argued in a journal article, published in the early 1960s, the cogito shouldn't be understood as a logical inference but as a kind of performance, where the one performing it (reflecting on the experience of reflecting, for example, which is an instance of thinking) could not but be struck by the immediate insight that while thinking (say, reflecting in this case) one exists. The cogito, in other words, is a phenomenological event, grounded in experience, and not a stuffy logical argument.

In the Discourse on Method (1637) and in the Meditations on First Philosophy (1641), Descartes tells us that the cogito plays an important role in establishing the very possibility of knowledge. In the opening paragraph of the Second Meditation, he writes:

"Archimedes used to demand just one firm and immovable point in order to shift the entire earth; so I too can hope for great things if I manage to find just one thing, however slight, that is certain and unshakeable." (Second Meditation)

The analogy of Archimedes' lever is instructive. In order for a lever to do its thing, what gives the lever its ability to do work, is what engineers refer to as the lever's fulcrum. It is the fixed and immovable point around which the lever-stick rotates. Without it, you've got nothing more than a big old stick in your hands. Likewise, Descartes suggests, if he could secure just one thing that was absolutely and utterly true, something that could not be doubted, he could use it like a fulcrum. It would serve as a kind of anchor, around which he could build an entire system of knowledge. So, the significance of the cogito is that it serves as the anchor, or as the fulcrum, of Descartes' epistemology (theory of knowledge).

In a later book, the Principles of Philosophy (1644), Descartes says that although the first "truth" that one will stumble upon when philosophizing in an orderly way is the cogito, as in fact happened in the Meditations, the most fundamental item, the real anchor of any system of knowledge, is actually the insight that God exists. The trouble, he says, is that human beings are so discombooberated cognitively by the time they reach adulthood, that the insight into God's existence is obscured by other ideas. But once one has sorted things out, which can be done by way of a thoroughgoing philosophical investigation, the insight will come to the surface, so to speak. But before that can happen, the investigation, as it unfolds, will first yield the insight into one's own existence, where that comes upon one's reflecting, reflecting say, on the moment of reflecting.

If you need me to be clearer, let me know, and I'm happy to give this another go.