The Pashupatastra is an irresistible and most destructive personal weapon of Shiva, Kali and Adi Para Shakti, which can be discharged by the mind, the eyes, words, or a bow.
The Pashupatastra is capable of destroying creation and vanquishing all beings. This Weapon never to be used against lesser enemies.
A Narrative from Kisari Mohan Ganguli’s translation of Mahabharat regarding the power of Pashupatastra —
O thou of mighty arms, that weapon (Pashupatastra) is superior to the Brahma, the Indra, the Agneya, and the Varuna weapons. Verily, it is capable of neutralizing every other weapon in the universe. It was with that weapon that the illustrious Mahadeva had in days of yore, burnt and consumed in a moment the triple city of the Asuras. With the greatest ease, Mahadeva, using that single arrow, achieved that feat. That weapon, shot by Mahadeva’s arms, can, without doubt consume in half the time taken up by a twinkling of the eyes the entire universe with all its mobile and immobile creatures. In the universe there is no being including even the deities, that are incapable of being slain by that weapon.
In Mahabharata, only Arjuna possessed Pashupatastra. Arjuna obtained this weapon from Lord Shiva.
Arjuna’s penance for Pashupatastra :
Following the advice of Lord Krishna to go on a meditation or tapasya to attain this divine weapon, Arjuna left his brothers for a penance during the exile.
Arjuna traveled for a while before reaching the mountain Indra Keeladri, Vijayawada. Here he sat in meditation in the name of Lord Shiva. Arjuna managed to please Lord Shiva by his severe penance in just few months . His penance generated so much intense heat that was unbearable to all living creatures of earth which ultimately forced Lord Shiva to come to earth.
Lord Shiva appeared in the guise of a hunter and challenged Arjuna to a fight. In that fierce battle 8 forms of Lord Shiva defeated Arjuna.
Arjuna prayed to a linga, asking who is the wild hunter who puts him into shame, and placed a flower on top of the linga. When he turnaround he saw that the flower was on the top of the head of that hunter and he understood that the hunter is Shiva himself. At last Arjuna gratified Mahadeva in battle by showing his prowess, then the hunter (Shiva) transformed himself to show his real avatar and blessed Arjuna with the Pashupatastra. Shiva adviced Arjuna on the abilities of the weapon, as well as the judgement he must use while wielding it.
It’s worth mentioning that Arjuna never used Pashupatastra in the Kurukshetra war.