These are Lucretius' thoughts on dispelling religious belief (which is - according to Lucretius - chiefly caused by the fear of of what follows death):
This terror, then, this darkness of the mind,
Not sunrise with its flaring spokes of light,
Nor glittering arrows of morning can disperse,
But only Nature's aspect and her law,
Which, teaching us, hath this exordium:
Nothing from nothing ever yet was born.
-- Lucretius, Of The Nature Of Things (trans. William Ellery Leonard)
In other words, since no soul exists we need not worry about what we will encounter after death; we will encounter nothing because we will no longer exist.