A swearing-in is the short official ceremony where a person who has just won or been given a public job stands up, usually with one hand raised, and says out loud that they will do the job properly and follow the law. Presidents, judges, police officers, army officers, and new citizens all go through one. The promise itself is called an oath, and the ceremony is called the swearing-in because the old word for making a serious promise in front of God or the law is 'to swear'. This is a different meaning of 'swear' from the rude one — nobody is saying bad words here. The moment matters because the job does not really start until the promise is made; before the swearing-in you are the 'president-elect', after it you are the president. You often hear 'the swearing-in ceremony', 'his swearing-in', or 'attend a swearing-in'. It is used as a noun, and it can also appear before another noun, as in 'swearing-in ceremony'. The related verb phrase is 'swear in' — 'They swore her in this morning', 'She was sworn in as mayor'. The word is neutral and slightly formal; you meet it mostly in news reports rather than in daily chat.