**Credit to user Mark Edward from whom this text is taken at the end of a long answer to a related question.** 

https://christianity.stackexchange.com/questions/25794/what-is-the-scriptural-basis-for-the-conditionalist-doctrine-of-hell

Annihilationism

Where conditionalism defines human immortality as conditional upon a right relationship with God, annihilationism is defined as a direct punishment of death from God. Qualitatively, there is no distinction between 'death' and 'annihilation'; the latter word is used solely to clarify just what it is that 'death' consists of.

Again, on a broader level, annihilationists believe the bible teaches that humans who are ultimately unrepentant will suffer death / cessation of existence. Poetic idioms in the Psalms are said to accurately describe a lack of existence, prophetic metaphors are said to capture the essence of a lack of existence, and the 'plain meaning' of basic words are said to describe a lack of existence directly.

The final fate of the unsaved is:

To vanish like smoke (Psalm 37.20)

Like the snail that melts into slime, like the stillborn child that never sees the sun (Psalm 58.8)

Like smoke that is driven away, like wax melts before a fire (Psalm 68.2)

Like a dream when one awakes (Psalm 73.20)

Destroyed, wiped out all remembrance of them (Isaiah 26.14)

Stubble in a burning oven; leaving them neither root nor branch; ashes under the soles of the righteous' feet (Malachi 4.1-3)

Slaying of body and soul (Matthew 10.28)

Eternal punishment (Matthew 25.46)

Death (Romans 6.23)

Eternal destruction (2 Thessalonians 1.9)

Like Sodom and Gomorrah: turned to ashes, and condemned to extinction (2 Peter 2.6)

The second death (Revelation 2.11ff)