The wisdom behind jihad

In Arabic, the word jihad means striving and expending one’s
energy. 

In Islamic terminology, jihad means the Muslim striving to
make the word of Allaah supreme and to establish His religion on earth. 

The purpose of jihad in Islam is not to kill non-Muslims,
rather the purpose is to establish the religion of Allaah on earth, to
establish the rule of His sharee’ah, and to bring people forth from the
worship of other people to the worship of the Lord of all people, from the
injustice of other religions to the justice of Islam. Allaah says
(interpretation of the meaning): 

“And fight them until
there is no more Fitnah (disbelief and polytheism, i.e. worshipping others
besides Allaah), and the religion (worship) will all be for Allaah Alone”

[al-Anfaal 8:39]

Shaykh ‘Abd al-Rahmaan al-Sa’di said in his commentary on
this verse: 

Here Allaah states the
purpose behind fighting for His sake, which is not to shed the blood of the
kaafirs and take their wealth; rather the purpose is so that all religion
(worship) will be for Allaah alone, and the religion of Allaah will prevail
over all other religions, and everything that goes against that, whether it
is shirk or anything else – which is what is meant by fitnah – will be
repelled. If this purpose is achieved, there will be no killing or
fighting. 

Tafseer Ibn Sa’di, p., 98 

The kuffaar whom we fight will themselves benefit from jihad.
We strive against them and fight them so that they will enter the religion
of Allaah which is acceptable to Him, which will lead to their salvation in
this world and in the Hereafter. Allaah says (interpretation of the
meaning): 

“You (true believers in
Islamic Monotheism, and real followers of Prophet Muhammad and his Sunnah)
are the best of peoples ever raised up for mankind; you enjoin Al-Ma‘roof
(i.e. Islamic Monotheism and all that Islam has ordained) and forbid
Al‑Munkar (polytheism, disbelief and all that Islam has forbidden), and you
believe in Allaah”

[Aal ‘Imraan 3:110]

al-Bukhaari (4557) narrated that Abu Hurayrah (may Allaah be
pleased with him) said: “ ‘You are the best of peoples ever raised up for
mankind’ means: the best of people for people, you bring them with
chains around their necks until they enter Islam.” 

Ibn al-Jawzi said: What this means is that they captured (in
war) and chained as prisoners, but when they come to know the truth of
Islam, they enter it willingly and will thus enter Paradise. 

In the answer to question no.
20214we have mentioned the types of jihad, of which there are four: jihad
al-nafs (striving against one’s nafs or self); jihad al-shaytaan (striving
against the Shaytaan); jihad al-kuffaar (striving against the disbelievers);
and jihad al-munaafiqeen (striving against the hypocrites). 

In the answer to question no.
34647 we have stated the wisdom
behind jihad; please read this as it will answer your question. 

And Allaah knows best.