interpretation: putting an unintelligible utterance into speech the gathered church can understand
Both times this noun appears in the New Testament, it names a gift Paul lists for worship in Corinth: the interpretation that pairs with speaking in tongues. When someone speaks in a tongue, no one in the room understands it; the gift of interpretation is what makes that utterance intelligible and useful to everyone present. Paul's whole concern in these chapters is that what happens in worship should build people up, and a tongue cannot do that until it is interpreted.
The word itself was broad in everyday Greek. It could mean translating one language into another, explaining something obscure, or simply putting a thought into clear words. Paul uses the noun only for this church setting, so the corpus gives us a single usage rather than a spread of distinct senses. The deeper question, which the word alone cannot answer, is exactly what is being made clear: an actual foreign language being rendered, or a Spirit-prompted utterance being given understandable form. That question is genuinely debated and is recorded in the dispute below.
Whatever the precise mechanics, the point Paul presses is constant: interpretation exists so that the rest of the congregation can share in what was said and be strengthened by it.