Full Idea
'Natural theology' is the attempt to show that belief in God's existence can be defended with reference to reason or argument which ought to be acceptable to anyone, not simply to those who believe in God's existence.
Gist of Idea
'Natural theology' aims to prove God to anyone (not just believers) by reason or argument
Source
Brian Davies (Introduction to the Philosophy of Religion [1982], 1 'Other')
Book Reference
Davies,Brian: 'An Introduction to the Philosophy of Religion' [OUP 1993], p.9
A Reaction
I assume by 'reason or argument' he primarily means evidence (plus the ontological argument). He cites Karl Barth as objecting to the assumption of natural theology (preferring revelation). Presumably Kierkegaard offers a rival view too.