Waswas (in Arabic وسوس) in Islam is a term for "whispers from Shaytan". When a Muslim has some thoughts against Islam, he disregards them as waswas - a voice of Shaytan.

Waswas in the Qur'an

The Arabic word وسوس (waswas) in various forms appears 5 times in the Qur'an.

The first two refer to the story of Adam and Eve. The fa- prefix means "but" or "then".

But the Shaitan made an evil suggestion (فَوَسْوَسَ, fa-waswasa) to them that he might make manifest to them what had been hidden from them of their evil inclinations, and he said: Your Lord has not forbidden you this tree except that you may not both become two angels or that you may (not) become of the immortals.
But the Shaitan made an evil suggestion (فَوَسْوَسَ, fa-waswasa) to him; he said: O Adam! Shall I guide you to the tree of immortality and a kingdom which decays not?

Then one time it's a persons soul which whispers. The tu- simply indicates present tense, 3rd person, feminine, singular verb.

And We have already created man and know what his soul whispers (تُوَسْوِسُ, tuwaswisu) to him, and We are closer to him than [his] jugular vein

And two times in a short sura 114. The al- indicates definite article (before a noun). The yu- indicates present tense, 3rd person, singular, masculine verb.

114:1 Say: I seek refuge in the Lord of men,

114:2 The King of men,

114:3 The god of men,

114:4 From the evil of the retreating whisperer (ٱلْوَسْوَاسِ, al-waswasi)

114:5 Who whispers (يُوَسْوِسُ, yuwaswisu) into the hearts of men,

114:6 From among the jinn and the men.


Tafsir Al-Jalalayn says that the "whisperer" in 114:4 is Satan:

from the evil of the slinking whisperer Satan — he is referred to by the name of the action waswasa on account of his repeated engaging in it — who slinks away and recoils from the heart whenever God is mentioned
Tafsir Al-Jalalayn on 114:4

From this we can conclude that the concept of waswas (Satan whispering into Muslim minds) is described in the Qur'an, so it is definitely a part of the Islamic doctrine.

Waswas in hadith

Muslims are forgiven thoughts against Islam (the "whispers from Satan") as long don't act upon them and keep silent:

Narrated Abu Huraira: The Prophet (ﷺ) said, "Allah has accepted my invocation to forgive what whispers in the hearts of my followers, unless they put it to action or utter it."
Narrated Abu Huraira: The Prophet (ﷺ) said, "Allah forgives my followers those (evil deeds) their souls may whisper or suggest to them as long as they do not act (on it) or speak."
It was narrated that Abu Hurairah said: "The Messenger of Allah said: 'Allah, the Mighty and Sublime, has forgiven my Ummah for what is whispered to them or what enters their minds, so long as they do not act upon it or speak of it.'"

Most of the whispers come from urinating in a place for bathing:

It was narrated from 'Abdullah bin Mughaffal that the Prophet (ﷺ) said:

"None of you should urinate in the place where he bathes, for most Waswas (devilish whispers) [1] come from that." [1] I.e., with regard to whether the urine has soiled his body or not.

Satan runs away farting, then comes back and whispers into hearts of Muslims when they pray, so they don't know how many rakats they have done:

It was narrated that Abu Hurairah said: "The Messenger of Allah (ﷺ) said: 'When the call to prayer is given, the Shaitan runs away breaking wind loudly. When the Tathwb (Iqamah) is completed, he comes back and whispers to a man in his hear, until he does not know how many (rak'ahs) he has prayed. If any one of you notices that, let him prostrate twice.'"

But when Muhammad forgets how many rakats he has done during prayer, it is because he is just a human being (and it doesn't seem to be a product of Satan whispers):

It was narrated that Ibrahim bin Suwaid said:

"Alqamah prayed five (rak'ahs) and was told about that. He said: 'Did I really do that?' I nodded yes. He said: 'What about you, O odd-eyed one?' I said: 'Yes'. So he prostrated twice, then he narrated to us from 'Abdullah that the Prophet (ﷺ) prayed five (rak'ahs), and the people whispered to one another, then they said to him: 'Has something been added the prayer?' He said: 'No.' So they told him, and he turned around and prostrated twice, then he said: 'I am only human; I forget as you forget.'"


Muhammad sprinkled water on his "private parts", so that he doesn't get whispers from Satan:

It was narrated from Al-Hakam, from his father, that when the Messenger of Allah (ﷺ) performed Wudu', he would take a handful of water and do this with it. Shu'bah described it: "He would sprinkle his private parts with it." [1] Shaikh Ibn As-Sunni said: "Al-Hakam (one of the narrators) is Ibn Sufyan Ath-Thaqafi. [1] The purpose is to ward off devilish whispers lest the person think any emission has taken place, and thus think that his Wudu' has been invalidated.

Soothsayers make accurate predictions thanks to hearing waswas:

Aishah (May Allah be pleased with her) said: Some people asked the Messenger of Allah (ﷺ) about soothsayers. He (ﷺ) said, "They are of no account." Upon this they said to him, "O Messenger of Allah! But they sometimes make true predictions." Thereupon the Messenger of Allah (ﷺ) said, "That is a word pertaining to truth which a jinn snatches (from the angels) and whispers into the ears of his friend (the soothsayers) who will then mix more than a hundred lies with it."
Riyad As-Salihin 18:1668

Waswas is a sign of faith:

It is narrated on the authority of Abu Huraira that some people from amongst the Companions of the Apostle (ﷺ) came to him and said:

Verily we perceive in our minds that which every one of us considers it too grave to express. He (the Holy Prophet) said: Do you really perceive it? They said: Yes. Upon this he remarked: That is the faith manifest.

Critical thinking

In the waswas-avoiding philosophy, you don't gather all information and then make rational conclusions. You gather only information which is in line with Islam, and everything which is not in line with Islam (regardless if it's true and logical) is dismissed. This creates a confirmation bias in Muslim minds.

For example, when Muslims try to prove that Allah exists, they often try the creationist argument, that "the world exists, therefore somebody must have d it". And now the question "Who created Allah then?" destroys their argument. But their argument was in line with Islam and this counter-argument is against Islam, so the first one continues to be widely accepted, but the counter-argument is dismissed as "waswas":

It is narrated on the authority of Abu Huraira that the Messenger of Allah may peace be upon him) observed: The Satan comes to everyone. of you and says: Who created this and that? till he questions: Who created your Lord? When he comes to that, one should seek refuge in Allah and keep away (from such idle thoughts).

So the waswas concept is against the concepts like critical thinking and logic.

Blind faith

The concept of waswas is a perfect method to keep people believing blindly in false information, because if their beliefs were false, they would never realize that, because everything which leads to the realization would be considered waswas.

Islamic treatment of waswas

When you search the web, you will find many Muslims trying to "cure" themselves from waswas [1]. The basic treatment method is ruqya - exorcism. Verses from the Qur'an are recited on the "posessed" Muslim. There is also a possibility of self-ruqya [2], where Muslim tries to get rid of waswas by praying and reading the Qur'an (and other practices).

Psychology

The waswas-avoiding behavior could probably be best described, in a secular way, by the psychological repression theory. A Muslim represses his "bad" thoughts. He pushes them out of his consciousness, into the unconscious mind. From the unconscious mind, the repressed thoughts might express themselves in dreams or as inner voices.

The therapy for psychological repression basically the opposite of what "Islamic therapy" does. In Freud's psychotherapy, the psychotherapist re-introduces the repressed thoughts back into the conscious mind [3]. The conscious mind then learns to live with the repressed thoughts and so there is no more repression. While the Islamic treatment of waswas is trying to repress the "bad" thoughts so much that they become silent. Which is not possible, because repressed thoughts don't disappear. They only hide in the unconscious mind and there they still affect a person's behavior and cause psychological problems.

Conclusions

  1. Just Google "waswas".
  2. http://www.aburuqya.com/self-ruqya
  3. Freud, Five Lectures p. 35