It is Waajib for every Muslim male and Muslim female who:-
has attained puberty (Baaligh)
is of sound mind (not insane)
possesses Nisaab for that moment in time, not necessarily for one Islamic calendar year (Nisaab is the value of excess wealth which makes a Muslim liable for Zakaah i.e. The possession of, or equivalent capital value of seven and half tolas gold (+ -3 ounces) or fifty two tolas of silver (+ - 20 ounces)
To make sacrifice in the Name of Allah
It is Waajib according to Imam-e-Azam Abu Hanifa (radi Allahu anhu) and Sunnat-e-Mu'akidda according to other Imams for Muslims to make Qurbani.
It is Waajib only for each Muslim male and female to make Qurbani for himself or herself; and not Waajib for him or her to make Qurbani for any other member of his or her family. It is only his or her duty to guide or instruct them to make Qurbani if they meet with the conditions of item in 1. above.
In the same manner as Sadaqat-ul-Fitr, Qurbani is a Waajib obligation for Muslims every year on the occasion of Eid-ul-Adha. It is not a once in a life-time duty.
It is permissible to make Qurbani in the name of Rasoolullah (sallal laahu alaihi wasallam) and his Ummah or any other deceased Muslim as a Nafil Qurbani on condition that the person making the Nafil Qurbani has discharged his obligation in his own Waajib Qurbani first.
It is not Waajib or necessary for the following people to make Qurbani:-
one who has not attained puberty (not Baaligh) even if he or she possesses Nisaab.
A traveller (who is not yet Muqeem).
One who does not possess Nisaab during that specific period in time.
On who may be in possession of Nisaab bit has turned insane.
Any Muslim male or female who is not liable for Qurbani but purchases an animal for Qurbani for the sake of Almighty Allah, then the Qurbani becomes Waajib for him.
Qurbani cannot be undertaken on behalf of another person upon who Qurbani is Waajib, without his or her prior consent.