Death involves the separation of the soul from the body (for the sake of clarity let’s call this the “first” death). The “second death” involves the separation of people from God (see also Revelation 20:6, Revelation 20:14; Revelation 21:8) and so is descriptive of being cast into hell. Christ promises that this horrible separation will never afflict those who conquer.
11 He who has an ear, let him hear what the Spirit says to the churches. The one who conquers will not be hurt by the second death.’