THE VERSE "BISMILLAHIR RAHMANIR RAHIM"

Whenever we recite a verse from the Holy Quran, we start with Bismillah, i.e. Bismillahir Rahmanir Rahim. The verse means, "In the Name of Allah, the Most Beneficent, the most Merciful."

The verse appears 114 times in the Holy Quran. It appears at the head of all the Suras except for Surah al-Bara'ah (Tawbah) where the Bismillah is not recited.

This is for two reasons. The first is that it is believed that the Surah is a continuation of the previous Surah, al-Anfal.

Another reason may be that the Surah contains very stern commandments against the idolaters and hypocrites and curses them.

In Surah an-Naml (the Ant), the Bismillah appears twice, once at the head of the Surah, and once as verse 27:30:

"She (the queen Bilqis) said, "O’ chiefs, verily, an honourable letter has been delivered to me. It is from Sulayman, and it says, "In the name of Allah, the Beneficent, the Merciful; Do not exalt yourselves against me, and come to be as those who submit (themselves to Allah)." (an-Naml, 27:29-31)

Tafsir

Imam Ja’far as Sadiq (A) has said about Bismillah:

The "Ba" is derived from "Baha-allah", the Splendour of Allah.
The "Seen" is derived from "Sana-allah", the Majesty of Allah.
The "Meem" is derived from "Mulk-allah" the Kingdom of Allah.
"Allah" is the God of everything.
"Ar Rahman"is the One Who is Merciful to all His creation.
"Ar Rahim" is the One Who singles out those who believe in Him to receive the greatest share of His mercy.

The words Rahman and Rahim are essentially from the same root word meaning mercy or grace. Yet in their application, they mean a different aspect of Allih’s mercy.

He is Rahman to all His creation, whether they be obedient to Him or disobedient.

He is Rahim to the faithful Muslims who do good and receive His mercy as a reward, both in this world and the next.

Is Bismillah part of the Suras of the Holy Qur'an

Merits of reciting Bismillah

The Holy Prophet (S) has said that when a teacher teaching a child to recite the Holy Quran tells the child to recite "Bismillahir-Rahmanir-Rahim", and the child recites it, Allah will decree a clearance for the child, for his parents, and for the teacher, from hell. He also said that the verse is comprised of nineteen letters, the same number as the number of the keepers of the gates of hell; therefore, whoever pronounces it, Allah will permit these letters to close the gates of hell against him.
To begin any good deed with the Bismillah means that you are asking Allah for His help in successfully completing the work. It also indicates your intention and reminds you that the work is undertaken solely for the pleasure of Allah. In other words, if a task is undertaken without reciting Bismilláh, it may be completed, but it does not earn His pleasure.

References:
Holy Quran, Tafsir of S. V. Mir Ahmed Ali
Ramadhan, Ahkam and Philosophy, Yasin T. al Jibouri