Meta as a prefix carries the meaning of ‘change’. (Metamorphosis is the process by which a caterpillar ‘changes form’ into a butterfly)
Noia comes from the word nous, which means ‘mind’.
Metanoia therefore means (literally) ‘a change of mind’ – but in our Bibles this is the word normally translated as ‘repentance’. Similarly, metanoeo means ‘I change my mind’ or ‘I repent’.
‘Repentance’ is a rather technical word – a piece of religious jargon. So it can be unhelpful to use it when talking to unbelievers. What does it mean in everyday language? Literally, it means to change your mind: to think differently, to change direction, to adopt a different attitude towards God and towards Jesus. It does not mean just feeling sorry because of the consequences of one’s behaviour. Nor does it mean (at least, not in the first instance) changing one’s behaviour! Of course, genuine repentance often does lead to sorrow over the wrongs that we have done in the past; and any genuine change in attitude will produce a change in behaviour. But we must not make the mistake of putting the cart before the horse! Deeds are the proof of repentance (Luke 3:8; Acts 26:20), not the repentance itself!
When Peter called on the crowd at Pentecost to ‘repent’ (Acts 2:38), it seems doubtful that he had in mind any specific individual sins (even though they must have committed many and various sins). He was exhorting them to change their attitude towards Jesus – to recognise the One that they had crucified as their Messiah. If they did so, certain consequences would inevitably follow: they would acknowledge Jesus as their Lord, obey His command to be baptised (verse 41), and thereafter put His teaching into practice (as we find them doing in Acts 2:42-47).
This emphasis on inward change is the very essence of Christianity. The Old Covenant failed because it was based on an external law that could deal only with external behaviour (if indeed it was kept at all). But Christians have been “made new in the attitude of our minds” (Ephesians 4:22-24). This means not that we will never sin again, but that we have changed our attitude to sin. Instead of acquiescing in it, or even enjoying it, we fight against it with the help of the Holy Spirit (Romans 8:5; Galatians 5:16,17). We will not always succeed, because we still have a sinful nature; but failure does not mean that our initial repentance was not genuine.