Muslims say Subhan Allah, Alhamdulillah and Allahu Akbar for 33 times after each daily prayer (salat). What do these words mean and what is the reason for saying them?
Also, why exactly 33 times ?
All Praise to Allah Subhanahu wa Taala and blessings of Him be on Prophet Muhammad peace be upon him His family and companions,
Subhan Allah (سبحان الله) means "Allah is free from imperfection".
Al-hamdu lillah (الحمد لله) means "All praise is due to Allah".
Allahu Akbar (الله أكبر ) means "Allah is Greatest".
Prophet Muhammad peace be upon him has said that these are some of the dearest phrases of Allah Swt and and has lot of benefits in reciting these,
Ka'b bin 'Ujrah (May Allah be pleased with him) reported: The Messenger of Allah (ﷺ) said, "There are some words, the reciters of which will never be disappointed. These are: Tasbih [saying 'Subhan-Allah' (Allah is free from imperfection)], thirty-three times, Tahmid [saying 'Al-hamdu lillah' (praise be to Allah)] thirty-three times and Takbir [saying 'Allahu Akbar' (Allah is Greatest)] thirty-four times; and these should be recited after the conclusion of every prescribed prayer."
It was narrated from Nu'man bin Bashir that : the Messenger of Allah (ﷺ) said: "What you mention of glory of Allah, of Tabsih (Subhan-Allah), Tahlil (Allahu-Akbar) and Tahmid (Al-Hamdu lillah), revolves around the Throne, buzzing like bees, reminding of the one who said it. Wouldn't any one of you like to have, or continue to have, something that reminds of him (in the presence of Allah)?'"(Ibn Majah)
And Also know as Tasbih Fatima
Narrated Ali bin Abi Talib Fatima came to the Prophet (ﷺ) asking for a servant. He said, "May I inform you of something better than that? When you go to bed, recite "Subhan Allah' thirty three times, 'Al hamduli l-lah' thirty three times, and 'Allahu Akbar' thirty four times. `Ali added, 'I have never failed to recite it ever since." Somebody asked, "Even on the night of the battle of Siffin?" He said, "Even on the night of the battle of Siffin."(Bukhari)
Narrated Abu Huraira: Some poor people came to the Prophet (ﷺ) and said, "The wealthy people will get higher grades and will have permanent enjoyment and they pray like us and fast as we do. They have more money by which they perform the Hajj, and `Umra; fight and struggle in Allah's Cause and give in charity." The Prophet said, "Shall I not tell you a thing upon which if you acted you would catch up with those who have surpassed you? Nobody would overtake you and you would be better than the people amongst whom you live except those who would do the same. Say "Subhana l-lah", "Al hamdu li l-lah" and "Allahu Akbar" thirty three times each after every (compulsory) prayer." We differed and some of us said that we should say, "Subhan-al-lah" thirty three times and "Al hamdu li l-lah" thirty three times and "Allahu Akbar" thirty four times. I went to the Prophet (ﷺ) who said, "Say, "Subhan-al-lah" and "Al hamdu li l-lah" and "Allahu Akbar" all together [??], thirty three times."(Bukhari)
And offcourse there would be some wisdom in the number 33 known to Allah Swt and His Messenger and in some narrations we see Prophet Muhammad peace be upon him has given this tasbih to recite 10 times as well,
Anas bin Malik narrated that : Umm Sulaim came upon the Prophet and said: "Teach me some words that I can say in my Salat." So he said: "Mention Allah's Greatness (saying: Allahu Akbar) ten times, mention Allah's Glory (saying: Subhan Allah) ten times, and mention Allah's praise (saying: Al-Hamdulilah) ten times. Then ask as you like, (for which) He says: 'Yes. Yes.'"(Tirmidhi)
Allah Swt and His Messenger knows best.