Praise be to Allaah.

Firstly: 

Remembering Allaah (dhikr) is one of the noblest deeds that a Muslim can do. Dhikr is not only verbal; rather we may remember Allaah in our hearts, on our lips and in our physical actions. 

Shaykh ‘Abd al-Rahmaan ibn Sa’di (may Allaah have mercy on him) said: 

The phrase dhikr Allaah (remembrance of Allaah) includes everything by means of which a person may draw close to Allaah, such as belief (‘aqeedah), thoughts, actions of the heart, physical actions, praising Allaah, learning and teaching beneficial knowledge, and so on. All of that is remembrance of Allaah. 

Al-Riyaadh al-Nadrah, p. 245 

Shaykh Ibn ‘Uthaymeen said: 

Remembrance of Allaah (dhikr) may be in the heart, on the tongue or in one’s physical actions. The basic principle is remembrance in the heart as the Prophet (peace and blessings of Allaah be upon him) said: “In the body there is a piece of flesh which, if it is sound, the entire body will be sound, but if it is corrupt the entire body will be corrupt. It is the heart.” Narrated by al-Bukhaari and Muslim. What counts is remembrance in the heart, because Allaah says (interpretation of the meaning): 

“and obey not him whose heart We have made heedless of Our remembrance, and who follows his own lusts”

[al-Kahf 18:28]

Remembering Allaah with one's tongue or physical actions without remembering Him in one's heart is a serious shortcoming; it is like a body without a soul. 

Remembering Allaah in one's heart means thinking about the signs of Allaah, loving Him, venerating Him, turning in repentance to Him, fearing Him, putting one's trust in Him, and other actions of the heart. 

Remembering Allaah on one's tongue means speaking all words that will bring one closer to Allaah, above all saying Laa ilaaha ill-Allaah. 

Remembering Allaah with one's physical actions means every deed which brings one closer to Allaah, such as standing, bowing and prostrating in prayer, engaging in jihad, paying zakaah. All of these are remembrance of Allaah, because when you do them you are obeying Allaah. Hence you are remembering Allaah when you do these actions. Hence Allaah says (interpretation of the meaning): 

“and perform As‑Salaah (Iqaamat‑as‑Salaah). Verily, As‑Salaah (the prayer) prevents from Al‑Fahsha’ (i.e. great sins of every kind, unlawful sexual intercourse) and Al‑Munkar (i.e. disbelief, polytheism, and every kind of evil wicked deed) and the remembering(praising) of (you by) Allaah (in front of the angels) is greater indeed [than your remembering (praising) of Allaah in prayers]”

[al-‘Ankaboot 29:45]

One of the scholars said: this means that what prayer includes of remembrance of Allaah is more important. This is one of the two scholarly views concerning this verse. 

Tafseer Soorat al-Baqarah, 2/167, 168. 

Secondly: 

With regard to the adhkaar which are spoken on the tongue, such as reciting Qur’aan, saying tasbeeh (Subhaan Allaah – glory be to Allaah), tahmeed (al-hamdu Lillaah – praise be to Allaah) and tahleel (Laa ilaaha ill-Allaah – there is no god but Allaah), and the dhikrs to be recited in the morning and evening, when going to sleep, when entering the washroom, and so on, it is essential to move the tongue, and a person is not regarded as having said them if he does not move his tongue. 

Ibn Rushd narrated in al-Bayaan wa’l-Tahseel (1/490) that Imam Maalik (may Allaah have mercy on him) was asked about a person who recites when praying, but no one can hear him, not even himself, and he does not move his tongue. He said: “This is not recitation, rather recitation is that in which the tongue moves.” End quote. 

Al-Kasaani said in Badaa’i’ al-Sanaa’i’ (4/118) 

Recitation can only be done by moving the tongue to say the sounds. Do you not see that if a worshipper who is able to recite does not move his tongue, his prayer is not acceptable? Similarly he swears that he does not recite a soorah from the Qur’aan but he looks at it and understands it but he does not move his tongue, then he is not breaking his oath. End quote. i.e. because he has not recited it, rather he has only looked at it.  

This is also indicated by the fact that the scholars said it is not allowed for a person who is junub to recite Qur’aan with his tongue, but they said it is permissible for him to look at the Mus-haf and recite Qur’aan in his heart, without moving his tongue. This indicates that there is a difference between the two things, and that not moving the tongue is not counted as reading or reciting. 

See al-Majmoo’, 1/187-189 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: Is it obligatory to move the tongue when reciting Qur’aan in prayer or is it sufficient to say it in one's heart?

 He replied: 

Recitation must be done with the tongue. If a person recites it in his heart when he is praying, that is not sufficient. The same applies to all other adhkaar; it is not sufficient to recite them in one's heart, rather it is essential to move one's tongue and lips, because they are words to be spoken, and that can only be achieved by moving the tongue and the lips. End quote. 

Majmoo’ Fataawa Ibn ‘Uthaymeen, 13/156 

And Allaah knows best.