A meaningful coincidence is when an event occurs randomly with some kind of spooky overtone. There's no such thing as a meaningful coincidence. Meaningful 'coincidences' are either pre-planned to deliberately spook out people of a gullible disposition¹ or belief in things of a spooky nature², or else are just completely random coincidences, and about as meaningful as any relationship that you are likely to develop with a woman named Mistress Cruella.

Coincidence, like beauty and ugliness, is in the eye of the beholder. A coincidence may go unreported, thereby invalidating it's existence. Coincidences are there to be perceived: if not reported and interpreted, they are simply random events.

A coincidence (meaningful or not) can be defined as a completely random event that coincides with another completely random event. Coincidences happen to millions upon millions of people every day. But then, coincidences fail to happen to these people, and everyone else: things which might have happened, but didn't. You might bump into someone in a shop who you haven't met for years, but a different person who you also haven't seen for years may just walk past the shop doorway. You missed the second person, but coincidentally met the third. Things like this can get very confusing. People who find life difficult to cope with are instructed to try turning to alcohol.

Really good example of a coincidence

Multiple scenarios: what could happen as the result of different coincidences.

1. Person A, let's call him Alan, goes to catch a train at time point 1 (TP1) in order to get to London to see his friend, Person B (Boris), in order to arrange the stag night for his marriage to Person C (Carol). As he gets on the train at TP1, he meets Person D (Debbie), an old flame, and they get chatting. When the train stops, at TP2, A and D are so deep in conversation that they do not notice any of the people around them getting off and changing trains. In fact, at TP3, London, when they are both supposed to get off, A is having serious doubts about marrying C, and decides to run off with D. B then comforts C, one thing leads to another, and after a long engagement, they get married, and eventually have a son, who goes on to theological college and becomes a vicar.
2. Person A goes to catch a train at TP1, in order to get to London to see his friend, Person B in order to arrange the stag night for his marriage to Person C. As he gets on the train, he stumbles slightly, and doesn't notice person D getting on as well. He sits down next to a deaf old war veteran, Person E (Edwin), and falls asleep after having a lecture on the North African campaign and the difficulty of extracting sand from between one's buttocks while under a full artillery barrage. At TP2, A jerks awake, and notices that E is no longer breathing. He alerts the rest of the train, and the driver, and rings an ambulance on his mobile phone. He comes with the old man to hospital, and gets off with a friendly nurse named Francine (Person F to you and me). A runs off with F, E snuffs it, D wanders off and gets on with her own business, eventually becoming a big noise in the advertising business, and B comforts the distraught C and marries her after a long engagement. B and C have one child, who turns out to be the Antichrist, the Four horsemen ride the skies and the end is nigh.
3. Person A goes to catch a train at TP1, in order to get to London to see his friend, Person B in order to arrange the stag night for his marriage to Person C. As he gets on the train at TP1, he meets Person D, an old flame. They get chatting, but at TP2, Person E bumbles into the carriage and disrupts their conversation by lecturing them on the North African campaign and the difficulty of extracting sand from between one's buttocks while under a full artillery barrage. A gets off the train, promising to ring D, but E blows his nose upon the piece of paper with her number on it. A gets off the train and waits for a taxi at TP3, he gets hit by an ambulance that was heading to pick up Person E, who had collapsed on the station floor, and dies. B comforts C, and marries her after a long engagement. B and C have one child, who goes on to become a successful taxi driver and actor, and appears in three episodes of 'The Bill'. D is mortified when A doesn't call her, and commits suicide. A and D beat the s**t out of E on the ethereal spirit plane when they found out what has happened. F dies alone and unloved, and marries deity G (God) and lives happily ever after.
4. Person A gets the bus.