Why does Islam have the concept of Jihad or Holy war, which some use to justify violence and terrorism?

Islam and Peace
Islam comes from the root word Salaam, which means peace. It also means submitting one's will to Allah (swt). The word Salaam is also an attribute of God. In this context, it means ‘The Giver of Peace'.
Muslims greet each other with Assalaamu alaikum which translates to wishing peace for one another. Even when wronged, the Glorious Qur'an advises Muslims to struggle against the temptation for hostility: And not alike are the good and the evil. Repel (evil) with what is best, when lo! he between whom and you was enmity would be as if he were a warm friend... [Al-Qur'an 41:34]
The Qur'an refers to Paradise as the “abode of peace”. Thus peace is a goal that Muslims are required to strive for, in their own selves, in their families and in their communities. It is ironical therefore, that Islam is perceived by many as being the motivation behind the wanton killing of innocent people.
Definition of Jihad
While Islam in general is misunderstood in the western world, perhaps no other Islamic term evokes such strong reactions as the word Jihad.
The word Jihad is mistranslated as “Holy War”. The Arabic equivalent of “Holy War” is harb-u-muqadasah. This term is not found in any verse of the Qur'an. There is nothing in the Islamic sources that permit a Muslim to fight against non-Muslims solely on the basis that they are not Muslim.

The word Jihad comes from the root word jahada, which means to struggle. At the individual level, jihad primarily refers to the inner struggle of being a person of virtue and submission to God in all aspects of life.
At the collective level, jihad can take various forms, such as:
1. Intellectual Jihad, which comprises of the struggle to convey the message of God to humankind and to combat social evils through knowledge, wisdom and dignified discourse. As the Glorious Qur'an says:
Who is better in speech than one who calls (men) to Allah, works righteousness, and says, "I am of those who bow in Islam”?
[Al-Qur'an 41:33]
2. Economic Jihad, which comprises of economic measures, and spending from one's means to improve the living conditions of the poor and the downtrodden.
3. Physical Jihad, which involves collective armed self-defense, as well as retribution against tyranny, exploitation, and oppression.
Thus the concept of Jihad is vast and comprehensive. Admittedly, it's the last category of Jihad that is a cause for concern to many, and which we shall explore in detail.