The second death is eternal separation from God for the unsaved. You can read about this in Revelation 2:11; 20:6, 14-15, and 21:8. The first death referred to in Matthew 10:28 is the physical death.
“He who has an ear, let him hear what the Spirit says to the churches. He who overcomes shall not be hurt by the second death”‘ (Revelation 2:11).
“Blessed and holy is he who has part in the first resurrection. Over such the second death has no power, but they shall be priests of God and of Christ, and shall reign with Him a thousand years” (Revelation 20:6).
“Then Death and Hades were cast into the lake of fire. This is the second death. And anyone not found written in the Book of Life was cast into the lake of fire” (Revelation 20:14-15).
“But the cowardly, unbelieving, abominable, murderers, sexually immoral, sorcerers, idolaters, and all liars shall have their part in the lake which burns with fire and brimstone, which is the second death” (Revelation 21:8).