Can someone explain to me this text passage? What does it mean?"One time as a child, in a power-failure, his mother had found and lit a last...

Yes, this is the story of a boy and his mother, alone in a power outage, with only candles to offer light.  It is an important passage in the novel because it shows us that all is not lost for Montag.  He once had the power of imagination and could enjoy a sense of wonder.  Years of being a firemen and years of not really thinking have robbed him of some of this.  Of course, it is Clarisse that re-awakens this power of imagination and sense of wonder in Montag.

It is also serves to foreshadow the novel's ending.  The city is destroyed while Montag and the other book men are sheltered in the woods.  The 'power' both literally (electricity) and figuratively (the government and entertainment) will be shut off.