I like Serena said:
Consider the effect of drugs, which makes us perceive the world differently than we would without drugs.
This reminds me of an argument I made in a philosophy class. My point was continuity in peoples perspectives of reality, as our senses aren't all wildly different, and if the professor is consistent in his appearance (dress, hair, beard style) for 4/5ths of the semester, everyone, using their relative senses, would clearly notice something wrong if on the last week he came in dressed as a clown.
However, with no continuity there is no reality. We may as well all have wildly different senses leading us to totally different interpretations of our observed reality as though every student was randomly dosed throughout the semester with LSD. The continuity of each and every students perceptions would conflict as the synesthesia effected everyone uniquely, and equal argument over what was what (agreement on an observable phenomenon within a group) would override their ability to, more or less, perceive through the senses in a stable and non-chaotic manner.
That said, Einsteins quote makes the most sense (to me) when referenced with what I've said. For me, it is an illusion, but when we perceive the illusion primarily the same as every other human save for a small percentage... then it is reality. If we all function with fluctuating and random brain functions similar to being drugged or being mentally ill, the 'illusion' of reality as a continuous perception capable of being shared and recognized (continuity) by everyone is gone and what we currently see as reality would be an illusion... since all our drugged up crazy pill breakfast minds wouldn't allow for a reality.
In a very late at morning attempt to tie all that in... science has that issue. Empirical evidence requires continuity, but the truth of what we know is really always an illusion until we can take it in and view it. Like the complex science of, "Is fire hot to the touch?"... let everyone hold their hand over a candle and try to pinch the flame (while assuming everyone understands what "hot" is), and the evidence will show in overwhelming results that fire is definitely hot.
More to the point, consider the effect of curved space. We don't actually see it, but we can do measurements and we can see the results of it.
Illusion or reality?
We only believe it to be reality, since the measurements are consistent and persistent.
The measurements being consistent and persistent = continuity (different but similar sense than I've used it). So introduce a medium like mathematics allowing scientists to measure what is invisible to the senses, but whoever understands the measurements is, in a smaller group compared to people as a whole, sustaining continuity. So... reality... A persistent illusion. If you factor out long periods of time (worlds flat, center of universe - etc).
