We perceive our surroundings via our sight, hearing and other senses. In most situations, perception is a straightforward process. It's raining. We see that it's raining. We reason that we don't want to get wet so we grab our umbrella.
Mistaken conclusions are discoverable and correctable through the same processes of perception and reasoning. This includes mistakes we associate with the perceptual process itself which we identify as illusions.
In everyday language, we describe illusions by making a distinction between the way things appear and the way things are. When we see a pencil partially submerged in water, we say that the pencil looks bent but is actually straight. This useful distinction enables us to avoid any confusion when talking about illusions.
With illusions there is no "bent pencil" that we perceive in our minds (recall that introspection is not a kind of observation) or perceive in the world. The takeaway lesson is that appearances can be deceiving, not that the "bent pencil" has a ghostly existence of its own that we somehow perceive.
I'll finish with a fascinating example of the color phi phenomenon that manages to combine both the illusion of motion and time travel. In the experiment, a red spot is lit for 150ms and then turned off. A short distance away, and 50ms later, a green spot is lit for 150ms and then turned off. Surprisingly, the observers report seeing a red spot moving to the right, turning abruptly green at the half-way point (before the green spot is lit) and then moving to the final position before disappearing. [1]
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[1] "Consciousness Explained", p114, Daniel Dennett. The phi phenomenon is the illusion of movement which, for example, we experience when watching a movie consisting of rapidly changing static images.