The root word for “Shafa'ah is shaf which means “even” as compared to “odd”. Hence, Shafa'ah means to be linked and attached to something. Consequently, the reason why an intercessor is called “Shafi” is that he attaches the person interceded for to himself, meets his needs, and saves him. The technical meaning of “Shafa'ah” is to help someone by negotiating on his behalf and asking the judge, or the ruler or the like for some kind of exemption, or forgiveness on the Day of Resurrection, with Allah's permission, the intercessor will request Allah to save the one interceded for from Hell, and will help the latter to enter Paradise. 

Intercession is divided in two parts; Generative (Takwini) Intercession and Legislative (Tashri'i) Intercession. 

Generative Intercession: All the Causes intercede for their Effects in order to come into existence. The examples of this type of intercession are the growth of a delicate seed from soil into a strong tree, raising a feeble infant by his parents, and help to an ignorant person by a scholar etc.

Legislative (Takwini) Intercession: According to the Commander of the Faithful, Imam Ali (a.s.): Intercession is the wings of the one who asks for forgiveness.”

The philosophy of intercession is to give hope and dispel desperation to a person who commits a Greater Sin which results in hopelessness. Allah by His Infinite Wisdom offers intercession as an option. Intercession develops spiritual relationship with the Friends of Allah (Ahlul Bayt) which in turn increases his mental and spiritual growth and perfection. In the process, he will try to please them and attain divine satisfaction. 

The word “Shafa'ah” and its derivatives has been used in the Glorious Qur'an 30 times. 

The Ayahs that deny Intercession:

Surah al-Baqarah Ayah 254: “O' you who believe! Spend in the way of Allah out of Bounties We have provided for you, before the Day comes when no bargaining will avail you, nor friendship nor intercession, and the unbelievers; they are the wrong-doers.” But in the next Ayah, He grants intercession but by His Permission. Ayah 255 of Surah al-Baqarah (Ayatal-Kursi): “Who can Intercede in His Presence except with His Permission” 

The Ayahs that seemingly suggest Intercession being restricted to Allah:

Surah al-Ana'm Ayah 51: “Give this warning to those in whose hearts is the fear that they will be brought to judgment before their Lord: except for Him they will have no Protector, nor intercessor that they may be pious.” 

Ayahs that details the qualities of the Intercessors:

Surah al-Zukhruf Ayah 86: “And those whom they invoke other than Allah, have no power of intercession; only he who bears witness to the Truth, and they know Him.” They must be Monotheists. 

Ayahs that specifies the conditions for granting Intercession:

Surah al-Anbiyah Ayah 28: “And they offer no intercession except for those who are acceptable, and they stand in awe and reverence of His Glory.” It means only if Allah is satisfied with him.

Imam Ali (a.s.) said: “It is impossible to find any discrepancy in Qur'an. Surley some parts of the Noble Qur'an elaborate on its other sections, and some parts of it attest to its other sections.”

In a nutshell, Intercession is a definite and proven fact, and others are also entitled to intercede with Permission of Allah.

The Noble Prophet (s.a.w.a.s.) said: “My Intercession does not go to the one who underestimates the daily prayers.” 

The Infallible Imam Ali (a.s.) said: “There is intercession for us, and for those who love us.”

The Infallible Imam Jafar al-Sadiq (a.s.) said: “On the Day of Judgment, Allah will muster both the worshiper and the religious scholar (Infallible Imams)” 

On inquiry from Umar ibn Yazid, the Infallible Imam (a.s.) said: “All of you (Shias) shall enter Paradise by the intercession of the Noble Prophet (s.a.w.a.s.) or his successors on the Day of Judgment. But , by Allah I fear for you for the Barzakh.” 

Sources used:

The Glorious Qur'an, Nahjul Balagha, The Message of Islam by Ayatullah Nasir Makaram Shirazi

A Rational Approach to Wahabiism & The Eternal Charter by Allama Ja'far Subhani

Al-Khisal by Shaikh al-Saduq (r.a.), Al-Kafi by Yaqub al-Kulayni