In the name of Allah, the Beneficent, the Merciful
As-salamu'alaikum wa rahmatullahe wa barakahtahu
Respected Sister In Islam
Fardh Kifaya - It is the Fard, that if performed by some (a sufficient number), the obligation falls from the rest
Example: A group of Muslim brothers meet another group on the way to the masjid. It is their duty to convey the 'Salaam' to the other, and so if "one" brother amongst them was to convey the 'Salaam' then insha'allah ta'ala the rest will be relieved of this duty.
Fardh 'Ayn -It is the Fard that is a compulsory duty on every single Muslim to perform, [just] like praying and fasting.
Allah the Almighty, and Majestic says:
“
And fight them until there is no more Fitnah (disbelief and polytheism:i.e. worshipping others beside Allah) and the religion (worship) will all be for Allah alone (in the whole world)...“
(Surat al Anfal : Verse 39)
The Fitnah referred to in this ayah means Shirk as Ibn 'Abbas (radiallaahu 'anhu) and Siddi said:
“
When the Kufaar attack and control a [Muslim] country, the Ummah is endangered in its Religion, and it becomes susceptible to doubt in its belief. Fighting [the Kufaar] then becomes an obligation, to protect the Religion, the lives, the land and wealth.”
Elaborated at the link following, from the Book "Defence of the Muslim Lands" By Shaheed Dr. Abdullah Yusuf Azzam (rahimahullah)
http://jihaadulkuffaarin.jeeran.com/File232.htm
And Allah Ta'ala Knows Best
Wasalamu'alaikum Wa rahmatullahe Wa barakahtahu