Islam, a religion of mercy, does not permit terrorism. Allah, the Exalted says in the Quran: “Allah does not forbid you from showing kindness and dealing justly with those who have not fought you about religion and have not driven you out of your homes. Allah loves just dealers. (Quran, 60:8).
"Jihad" means struggling or striving. Jihad primarily refers to the inner struggle of being a person of virtue and submission to God in all aspects of life. Jihad is not holy war as it is popularly propagated in the media. The Prophet Muhammad (PBUH) said that the greatest jihad is to struggle with the insidious suggestions of one’s own soul.
"Ayshah, wife of the Prophet Muhammad (PBUH) asked, 'O Messenger of Allah, we see Jihad as the best of deeds, so shouldn't we join it?' He replied, 'But the best of Jihad is a perfect Hajj (pilgrimage to Makkah).'" [Sahih Al-Bukhari #2784]
On another occasion, a man asked the Prophet Muhammad (peace be upon him): "'Should I join the war and do Jihad?' He asked, 'Do you have parents?' The man said, 'Yes!' The Prophet (PBUH) said, 'Then strive by serving them!'" [Sahih Al-Bukhari #5972]
Yet another man asked the Messenger of Allah (peace be upon him): "'What kind of jihad is better?' He replied, 'A word of truth in front of an oppressive ruler!'" [Sunan Al-Nasa'i #4209]