Pertaining to an age, and especially to the age to come — hence 'eternal.' Aiōnios is the standard NT adjective for what belongs to God's realm and endures beyond time. It describes eternal life, eternal punishment, eternal glory, and the eternal God himself.
When Jesus speaks of aiōnios zōē (eternal life), He means not just unending duration but the quality of life belonging to the coming age — life in God's presence. 'This is eternal life: that they know you, the only true God' (John 17:3). The adjective also modifies judgment and punishment (Matthew 25:46), creating one of theology's most debated tensions: eternal life and eternal punishment use the same word.