An accounting term: to enter in a ledger, to credit to an account, to reckon something as belonging to someone. Paul uses it in Romans 4 to explain justification by faith — God 'credited' (elogisthe) Abraham's faith as righteousness. This is imputation: righteousness is legally attributed to the believer not because they earned it but because God credits Christ's righteousness to them.
Romans 4 uses logizomai eleven times as Paul hammers the point: Abraham was justified before his circumcision, by faith, not works. God 'reckons' righteousness to the ungodly (4:5) — the one who trusts the God who justifies. This is the ground of evangelical salvation: not moral achievement but divine accounting. Christ's righteousness is credited to us; our sin was credited to him (2 Cor 5:21 — the great exchange).