Question: Whenever I hear someone like, say, Daniel Dennett say that consciousness is an "illusion", I'm always left pretty much stumped. Firstly, both the terms "consciousness" and "illusion" are generally left undefined, although this is more apparent with the term "illusion". With this, I have to use the default definitions of these terms, "consciousness" being a somewhat self-explanatory "state of conscious awareness", and "illusion" being "a delusion of some sort". This is really where the main problem arises for me. How can one claim that consciousness is an illusion when the concept of "illusion" requires a subject to be deluded, which the original claim actively denies the existence of? Granted, this subject doesn't have to be an "I", but the denial of any decieved subject at all seems to negate the argument itself.

The other problem I have with the claim is that it seems to contradict the fairly self evident claim that, as Nietzsche put it, "It thinks, therefore it is".

Is the claim really as nonsensical as it seems, or am I missing something big? Perhaps the definition of a term or multiple terms?

Answer: 
This phrasing is used by different philosophers for different purposes, so one must take the phrase in context. However, in general, it is used in reference to the idea that consciousness is a thing which is separable from other things.

Denett argues that consciousness does not exist except as an image which describes the interplay of events within the brain. I use the word image here to avoid the loaded term "illusion." The key factor here is that the image is a depiction of the thing rather than the thing itself. Denett would argue that if one were to take this image and look for it in the real world, we would not find it. Instead we would find the interplay of events in the brain. In this sense, I might argue that his position is that consciousness is to reality as the number 1 is to the series {1/2, 3/4, 7/8, 15/16, ...}. It could be viewed as a limit were the process to be continued, but it never actually reaches that point. In his view, the reality never quite reaches the vaunted concept we call consciousness.

In this sense, the word illusion is chosen for pragmatic reasons. It instills the correct imagery in the minds of those who believe consciousness exists. For those who agree with Denett, the word must naturally shift meaning, for there is no consciousness to ascribe meaning to the word "illusion." There may be a self-consistent viewpoint regarding how the brain *really* works such that that phrase is interpreted correctly, but Denett may not call this out with extra words.

Other philosophers have used this concept for other reasons. Alan Watts, for instance, argues that no self is truly isolated from its environment. According to him, there is no consciousness which can be isolated from its environment and pointed at to say "this is a consciousness." He argues that "for every inside there is an outside." Thus there is no consciousness outside or isolated from its environment.
Your scepticism of Dennett is well-grounded. Claims similar to Dennetts were given by Skinner under the rubric of behavioral psychology where one supposed thinking things (*res cogitans*) were merely things, that is automatons, and one was not supposed to ask a man about his inner self, his *telos* or his intentions, or indeed how things were going with him, as one was supposed to merely observe his actions, his gestures, his attitudes and then tell him truly how things were going with him, his intentions, his purposes. 

These claims were blown apart by Chomsky who pointed out the chicanery of supposing human beings were to be studied as though they were merely objects of the disinterested scientific gaze - like rocks or laboratory rats. The chicanery goes deeper as it also sullies the good name of science by a methodology that simply doesn't stand up to any scrutiny. Likewise Dennett is sullying the good name of philosophy by dogmatically flogging a dead thought to a coterie of admirers who should know better - but don't - and to a larger audience who do know better but are cowed or over-awed by his linguistic gymnastics. 

Every language under the sun has the word 'I'. Self-awareness, self-consciousness exists. It's not an illusion. The only illusion here is that Dennett is doing good philosophy when he's doing bad philosophy.