First, it's what's called a constructor series. That is, there are different engine manufacturers and each team builds their own car. Soem components can be shared (ie bought from manufacturers), some can't. The cars are intentionally not identical. Some are just better. There are constraints but teams have a lot lf latitude.
This is as opposed to a spec series 9eg Formula E) where the cars are basically identical. This is a spectrum.
There are 10 teams (11 next year; there have been more in the past). Each team fields 2 cars with 2 drivers. The first 10 places award points (up to 25) to both the driver and the team. The team (constructor) standings at the end of the year award prize money. There is a title for the best team and the best driver.
The fact that there are 2 drivers and they both want to win the drivers championship. This creates a ton of tension and conflict.
Because there are only 20(ish) drivers in a season, the individual personalities matter. The complete polar opposite of this is probably the NFL, which has I believe ~1700 full time players in any given year, probably not even including practice squads.
There is now a constructor (and engine) cost cap. That's relatively new (since 2022). Before that some teams would spend 2-3x+ what other teams did, kinda like MLB.
So because there are unequal cars, there are periods of dominance. Currently the clear #1 car is fielded by McLaren. Previously that was Red Bull. Then for a long time it was Mercedes. Sometimes (notably in 2021) there was a close fight between 2 teams for both championships.
The current engine regulations are for a hybrid engine with ground effect cars. Next year it's even more hybrid but they're getting rid of ground effect.
There are currently 24 races in a season going from March to early December with some breaks in between. Race weekends generally run from Friday to Sunday. The format is to have 3 free practice ("FP") sessions on 2 days, each lasting an hour, where teams can change their setup, run different tires and have different run plans to fine tune their setup.
The second session on the Saturday is qualifying (often just "quali") in 3 sessions. In each session each driver is trying to do the fastest single lap possible. In the first 2 sessions the bottom 5 drivers are eliminated. They have a tire allowance for all this that I won't go into. But the starting order for the race (on Sunday) is set from fastest to slowest times. These sessions are called q1, q2 and q3.
The actual race typically runs ~300km (Monaco is less). With different lap lengths that's a different number of laps. In the current regulations the cars are fully-fueled at the start. Previously there was in-race refuelling but no more, for safety reasons.
Tires will last a varying number of laps and there are 3 compounds to use, called soft, medium and hard. There's more complexity to this but I'll ignore that. You have to use at last 2 differnt compounds in the race. That's what the pit stops are, to change tires and possibly a broken front wing (and, as I said, previously refuelling).
The starting order and finishing order are usually called p1 to p20. The top 3 places are also called podium places because, well, you get a trophy. On a podium.
There's more to it like sprint races and how wet weather changes things as well as safety procedures like safety cars, red flags and yellow flags.
But when you go beyond this, you get into the lore, which is both fascinating and hilarious, like industrial espionage on teams that was exposed by a Kinko's employee or someone intentionally getting a driver to crash to affect the world championship or the two childhood friends who ended up teammates and ended up not speaking to each other after a bitter championship fight.