close relationship; intimate bond; thick as thieves
Colloquial and somewhat rare; describes a very close, often romantic or deeply affectionate relationship. The word 濃い (thick, dense) metaphorically suggests a strong, inseparable bond. Compare with 恋仲 (こいなか), which specifically means 'in love with each other'.
See also: 恋仲
Those two seem to be really close.
He and I aren't just friends; we have a deep bond.
Compound of 濃い (こい, 'thick, dense, strong') and 仲 (なか, 'relationship'). The metaphorical use of 濃い to describe a close human bond is a natural extension of its meaning.