If there's one thing the genre of romance is known for, it's tropes. Romantic comedies (and just romantic films in general) have tropes that often show up and make these kinds of movies what they are. Sometimes discussion around tropes paints them negatively, but they're really beneficial for instances like this, where romance fans know exactly what they want to see, and are expecting these kinds of tropes on screen because they're what attract people to the story in the first place.
One of the most famous romance tropes is the meet-cute, where the protagonists/love interests see each other for the first time. There are a variety of ways that this trope can be executed, and it has shown up thousands of times across various romantic movies and TV shows. There's nothing more exciting in a rom-com than an adorably romantic (or perhaps awkward) first meeting, where the protagonist locks eyes with someone, not even knowing how important that person is about to become to them.
Meet cutes are the classic way to have two leading characters in a movie meet. The term actually originated in a 1938 film called Bluebeard's Eighth Wife, where the two main characters meet while shopping for pajamas and end up engaging each other in a cute conversation - which is where the name comes from. A lot of times, the interaction is somewhere on the spectrum of really awkward to really romantic, but any good meet cute is definitely memorable. It could be a comedic moment, or it could be love at first sight - it really just depends on the specific couple and on the tone of the movie.
Depending on the kind of romance, the characters either feel some sort of instant connection or they hate each other, in an enemies-to-lovers kind of storyline. For instance, take Harry and Sally in When Harry Met Sally, one of the most prime examples of a rom-com that exists. These two characters don't have a lot in common at first, and tend to argue a lot, but over the course of the story, they fall in love. This is one of the more interesting dynamics, as the audience gets to watch the progression from their negative experience during the meet-cute to a genuine romance.
Another classic meet cute trope is when one character is instantly smitten with the other, but that other character needs some time to come around. Maybe they're already dating someone else, or maybe they just outright dislike the other lead of the film, but for whatever reason, they don't immediately share the same feelings as the character who fell first. The main example of this is in The Notebook, as when Noah first meets Allie, he falls in love with her, but she already has a boyfriend. It gives the characters a conflict they have to work through, and allows the character who's not as interested to grow through the story as they gradually fall in love.
The most important thing about the meet-cute is that it properly sets up the romance. The writers want the audience to be invested in these characters, so they have to create some sort of tension between them that gets resolved over the course of the film, and this will often start with their first meeting. A rom-com or romance can fully hinge on how the audience feels about the meet cute, and whether or not they find the ensuing romance to be believable or not.
Other examples of the meet-cute include Love Actually, where multiple characters encounter their love interest in an unusual situation, such as how the Prime Minister meets Natalie while she's working on his staff, or how John and Judy meet while making an adult film. Titanic has a meet cute, though perhaps the exact circumstances are less than cute, as Rose is standing on the side of the ship about to jump before Jack stops her. The Holiday actually outright discusses meet-cutes as Kate Winslet's Iris has to have the term explained to her, which becomes ironic as the film itself includes major meet-cutes between its four main characters.
The meet-cute is one of the easiest ways to endear the main characters to the audience. These interactions can either be sweepingly romantic or painfully human, and either way, they make the viewer more interested in the journeys that these characters go on. While real-life romance might start mundanely, any good movie romance needs to hook the audience right away, and having the characters meet in some crazy, silly situation is the best way to do just that.