The Nemean Lion was a monster that had claws as sharp as swords and golden fur that could not be broken. He could not be killed by normal people.
There are two stories as to how Heracles killed the lion: the first is that Heracles simply used his hands and strangled the lion to death. The second is that he fired an arrow into its mouth – which was not strong like the fur – and the lion was killed.
After the lion was killed, Athena told Heracles to use the lion’s claws to cut off its fur. Heracles could then use this as a protective coat.
When King Eurystheus saw Heracles return he was afraid: he did not think Heracles would survive the first task. He told Heracles that the tasks were going to get harder, and that Heracles could not come inside the palace, but had to show he had completed the tasks from outside.