Vikalpa is one of the five varieties of fluctuations of the mind (vrittis) recognized in Yoga. Patanjali (Yogasutra I.9) has defined it as “that which issues from knowledge of words and has no corresponding object.”
Vikalpa Vritti is different from both true and false knowledge, although it has some similarity to both.
The phrase rajaputra (son of a king) is quite meaningful and would convey true knowledge in the presence of such a person. But the phrase vandhyaputra (son of a woman who is unable to bear children) which appears to be equally meaningful is not actually so, because we can find no such person in the world.
The individual terms making this phrase are indeed quite meaningful separately, but when combined together, the whole phrase falls to indicate any object as an actual existent. Such a phrase is called a vikalpa. It means an imagination or fanciful notion. Other examples of vikalpa are sasaringa (hare’s horn), hemadri (golden mountain) and Kshirasagara (ocean of milk).
Vikalpa differs from viparyaya (false knowledge) in that we cannot prove it to be false. When we take a rope to be a snake, it is an example of falsehood, which can be proved false after going near and touching it or after viewing it in proper light. Then the idea of the false object gets cancelled; it persists no more, and it is replaced by a true idea. But such a thing is not possible in case of a vikalpa, because there is no object which will replace it. The idea may be cancelled, however, and in that it does resemble falsehood.
Source –
The Science of Yoga (1988) – Aprabuddha – Shri Aprabuddha Vihara Sadhana
Yoga Psychology (1960) – Swami Abhedananda – Ramkrishna Vedanta Math Kolkata
Encyclopedia of Hinduism Volume XI page 347 - IHRF