A little long... but explains it really nicely:
The second degree is eemaan (faith), which in Arabic means belief which is committed to submission. In Islamic terminology its meaning varies according to usage and it may mean one of two things:
(i) When the word is used on its own and is not accompanied by the word Islam, it refers to the religion as a whole, as in the verses where Allaah says (interpretation of the meaning):
“Allaah is the Wali (Protector or Guardian) of those who believe. He brings them out from darkness into light”
“and put your trust in Allaah if you are believers indeed”
And the Prophet (peace and blessings of Allaah be upon him) said: “No one will enter Paradise except the believers.” Narrated by Muslim, 114.
Hence the salaf were unanimously agreed that eemaan means “affirming in the heart – which includes actions of the heart – and saying with the tongue and acting with one’s physical faculties. It increases by doing acts of obedience and decreases by committing sin.”
Hence Allaah limited the word eemaan to those who adhere to His religion in full, inwardly and outwardly, when He said (interpretation of the meaning):
“The believers are only those who, when Allaah is mentioned, feel a fear in their hearts and when His Verses (this Qur’aan) are recited unto them, they (i.e. the Verses) increase their Faith; and they put their trust in their Lord (Alone);
3. Who perform As-Salaah (Iqaamat‑as‑ Salaah) and spend out of that We have provided them.
4. It is they who are the believers in truth. For them are grades of dignity with their Lord, and forgiveness and a generous provision (Paradise)” [al-Anfaal 8:2-4]
And Allaah referred to eemaan as including all of that when He said (interpretation of the meaning):
“but Al-Birr is (the quality of) the one who believes in Allaah, the Last Day, the Angels, the Book, the Prophets and gives his wealth, in spite of love for it, to the kinsfolk, to the orphans, and to Al-Masaakeen (the poor), and to the wayfarer, and to those who ask, and to set slaves free, performs As-Salaah (Iqaamat-as-Salaah), and gives the Zakât, and who fulfil their covenant when they make it, and who are patient in extreme poverty and ailment (disease) and at the time of fighting (during the battles). Such are the people of the truth and they are Al‑Muttaqoon (the pious”
And the Prophet (peace and blessings of Allaah be upon him) referred to eemaan as including all of that in the hadeeth about the delegation of ‘Abd al-Qays which is narrated in Saheeh al-Bukhaari (53) and Saheeh Muslim (17), where he said: “I enjoin you to believe in Allaah alone. Do you know what belief (or faith) in Allaah alone is?” They said: “Allaah and His Messenger know best.” He said: “To bear witness that there is no god but Allaah and that Muhammad is the Messenger of Allaah, to establish regular prayer, to pay zakaah, to fast Ramadaan, and to give one-fifth of the war-booty (the khums).”
The Prophet (peace and blessings of Allaah be upon him) described fasting the month of Ramadaan out of faith and in the hope of reward as being part of faith; he also said the same concerning spending the night of Laylat al-Qadar in prayer, fulfilling one's trusts, jihad, Hajj, attending funerals, etc. In Saheeh al-Bukhaari (9) and Saheeh Muslim (35) it says: “Faith has seventy-odd branches, the highest of which is saying Laa ilaaha ill-Allaah (there is go god except Allaah) and the least of which is removing a harmful thing from the road.” It would take too long to mention all the verses and ahaadeeth that speak of this topic.
(ii) When the word eemaan is used in conjunction with the word Islam. In this case it is understood as referring to inward beliefs as in the hadeeth of Jibreel etc., and as in the hadeeth of the Prophet (peace and blessings of Allaah be upon him) concerning the funeral du’aa’: “O Allaah, whomever among us you cause to live, cause him to live in Islam, and whomever among us you cause to die, cause him to die in faith.” Narrated by al-Tirmidhi, 1-24; he said it is hasan saheeh. It was also classed as saheeh by al-Albaani, as stated in Saheeh Sunan al-Tirmidhi, 1/299. That is because physical actions can only be accomplished during life, but when one is dying all that is left is the words and actions of the heart.
The point is that when either word, eemaan or Islam, is used alone, there is no difference between them, rather each of them when used alone refers to the entire religion. If there is any difference between them, then the word Islam refers to outward physical actions and the word eemaan refers to inward actions of the heart. This is what is indicated by the hadeeth of Jibreel which was narrated by Muslim in his Saheeh (8) from ‘Umar ibn al-Khattaab who said:
One day when we were with the Messenger of Allaah (peace and blessings of Allaah be upon him), there appeared before us a man whose clothes were exceedingly white and his hair was exceedingly black, and there were no signs of travel on him. No one among us recognized him. He came and sat down by the Prophet (peace and blessings of Allaah be upon him) and rested his knees against his and placed the palms on his hands on his thighs. He said: “O Muhammad, tell me about Islam.” The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Islam is to testify that there is none worthy of worship except Allaah and that Muhammad is the Messenger of Allaah, to establish regular prayer, to pay zakaah, to fast Ramadaan and to go on pilgrimage to the House if you are able to.” He said: “You have spoke the truth.” And we were amazed at his asking that and saying that he had spoken the truth. Then he said: “Tell me about eemaan (faith, belief),” He said: “It means believing in Allaah, His angels, His Books, His Messengers, and the Last Day, and believing in al-qadar (the divine will and decree), both good and bad.” He said: “You have spoken the truth.” He said: “Tell me about ihsaan.” He said: “It means worshipping Allaah as if you can see Him, and although you cannot see Him, He can see you.” He said: “Tell me about the Hour.” He said: “The one who is being asked does not know more about it than the one who is asking.” He said: “Then tell me about its signs.” He said: “The slave-girl will give birth to her mistress, and you will see the barefoot, naked, destitute herdsmen competing in constructing lofty buildings.” Then he departed and I stayed for a while. Then he said to me: “O ‘Umar, do you know who the questioner was?” I said: “Allaah and His Messenger know best.” He said: “That was Jibreel, who came to teach you your religion.”