If something misleads or deceives you, it is illusive. If you think you see a unicorn in your back yard, but it suddenly disappears, you can describe the vision as illusive.
Illusive comes from illusion, an old, old word that originally meant "to mock, to make fun of, to trick." Magicians make great use of illusions, but while someone can be deliberately illusive, the word does not always imply that that someone means to mislead you. Some things, like truth, are illusive by nature; others, like the past, become hazy through time.