By Juno's hate urged on, Alcmena's Son,
At sixteen years his noble toils begun.
Nemæa's dreadful Lion first he sought,
The savage slew & to Eurystheus brought,
From his huge sides his shaggy spoils he tore,
Around him threw, & e'er in triumph wore.
The first of Hercules' twelve labours, set by Eurystheus (his cousin) was to slay the Nemean Lion and bring back its skin.
The Nemean Lion was a vicious monster in Greek mythology that lived in Nemea. The lion was usually considered the offspring of Typhon and Echidna, but it was also said to have fallen from the moon, offspring of Zeus and Selene. A third origin has it being born of the Chimera.
The lion had been terrorizing the area around Nemea, and had a skin so thick that it was impenetrable to weapons. When Hercules first tackled it, his weapons - bow and arrow, a club made from an olive tree (which he pulled out of the ground himself) and a bronze sword - were all ineffective. At last Hercules threw away his weapons and wrestled the lion to the ground, eventually killing it by thrusting his arm down its throat and choking it to death. (In some variants, Hercules actually strangled the beast, or broke its jaw.)
Hercules spent hours trying unsuccessfully to skin the lion, and gradually growing angrier as it appeared he would be unable to complete his first task. Eventually Athena, in the guise of an old crone, helped Hercules to realise that the best tools to cut the hide were the creature's own claws. Thus, with a little divine intervention, Hercules completed his first task.
Thereafter, he wore the impenetrable hide as armour.