"Just as people spoke about the triumph of democracy in the 90s, now people are talking about the end of democracy," says Mr Obama.
"We have to resist that cynicism. Because, we've been through darker times, we've been in lower valleys."
Mandela's story teaches us that we need to remain hopeful, he says.
"That journey [of Mr Mandela] was not easy. It was not preordained. The man went to prison for almost three decades."
And yet, Mr Obama says, his power actually grew while he was in jail.
"He knew if he stuck to what he knew was true... then it might not happen tomorrow, it might not happen next week, it might not even happen in your lifetime, but ultimately the better story can win out."
He says young people need to be "fired up".
"We don't just need one leader... what we badly need is that collective spirit," he says.
"So young people, my message to you is simple: keep believing, keep marching, keep raising your voice."
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