Why do we cast a circle? Well, there are a number of reasons why a person of any tradition or path may wish to cast one before their work commences. Most of the justifications can be summed up in three types: a circle of sacred space, a circle of power, and a circle of protection.
While all circles create a sacred space of some type, some create it purely for this reason alone. Typically, this type will be used exclusively on Sabbats, which are reserved for veneration of the gods and observation of the seasons within most Traditions, rather than magical feats. Some pagans that do not practice magic will still create one of these for religous practice.
When we cast that circle, we are creating a rift between the seen and unseen worlds. We are creating hallowed grounds in a place that exists and does not exist simultaneously. We are separating ourselves, in mind, body and spirit, from the everyday world and saying "This is where I and the gods do meet". It is here that below ascends to the above, and above descends below. Sacred space is equilibrium.
Besides devotional practices, a circle of this type may be created for the purpose of meditation, personal studies, or to 'get away from it all', stepping away from the hustle and bustle of life and into asylum found within its perimeter.
Circle of Power
Some circles are created for the purpose of magical operations. This circle acts as a vessel and retains the Will of the solitary or the Will of the collective in the coven and, magnifying it with action and invoked forces, is released for the maximal effect upon the intended aim. See: Cone of Power.
In most circles of power, conjurations of the elemental/divine 'quarters' (or, guardians, watchtowers, etc) are established in the four cardinal directions. This establishes some noteworthy events:
The four directions intersect and creates a crossroads within the circle. And, according to tradition, all witchcraft happens at the crossroads. The witch/magician who stands within the center then becomes the center axis and conduit upon which the forces are directed. This is one reason why the High Priestess and/or High Priest stands in the center.
Whenever you cast a circle, it becomes a lighthouse that beacons across the etherial worlds. This has the uncanny effect of attracting anything to its attention. Thus, the guardians make certain that the ritual proceedings are not influenced by outside, unwanted forces. They are the divine doormen that only allows the invited within and prevents the uninvited guest from crashing the party.
Sometimes, they are requested to 'lend their power' to a specific operation. They may be requested to bless and consecrate new tools- or, the new initiate. Their assistance amplifies the ritual and thus increases the certainty that one's Will be done.
It should be noted that the quarters are often established in a circle whose sacred space is purely devotional, too. In this case, they prevent external disturbance and also share in the communion with the gods.
The Circle of Protection
And, finally, the Witch or Magician may find cause in working with a particular entity of which one should hope to never have a direct encounter with elsewhere. Typically, we are talking about negative or chaotic spirits. Sometimes, even, it's not a negative entity, but rather one too overwhelming in presence and you want a buffer between you and the spirit. In all cases, you want to make certain that your circle is especially fortified. Archangelic and God-forms typically stand as guardian. You want to make damn sure that it cannot reach out and cop a feel on your magical rump at any point during the ritual.
Some of these circles can be lengthy in time to erect. Some may include physical boundaries, too, such as with salt or red brick dust, for extra protection. Invocations delivered to invest the magician with the authority of the divine are commonplace, and sometimes demands, backed by threats, are made to submit the spirit to your Will. In other cases, you simply need to ask the spirit, but you still want that partition between you two. Whatever the case, the circle must be flawless in its creation. An error could be quite disastrous.
Why would someone do all me this? For the same reason that a government might 'hire' criminals to do some dirty work. Sometimes, no others can quite do the work like an angry 'ghost' or something out of the belly of the underworld. Far more often than not, however, the vast majority of magic users will be without the need for this type.
That's it for the three major types in terms as why we would cast a circle. Any circle could be any combination of the above, but usually serves in one specific capacity.
For a more thorough look into the mechanics of a circle, I have posted my view here: