This has really evolved over time. Originally, there were single-game randomizers, which became more and more sophisticated in what they could randomize. Early on, those randomizers added "logic", meaning that they ensure you can't have an impossible random seed where an item is stuck behind a point that needs that item to proceed, or a set of items that would mutually require each other.
At some point, people started combining games; most notably, "SMZ3" is a two-game randomizer for Super Metroid and Link to the Past (already two very popular games for randomizers), in which you're playing one SNES cartridge that has both games on it and you can step in specific doors to switch from a spot in one game to a spot in the other game.
Archipelago is an evolution of those multi-game randomizers, which combines the logic from each game to ensure that someone is always able to proceed.
And there are options you can choose to make things simpler; for instance, you can prevent certain key items from being very late in the game. But it's also fun to not do that, and end up (say) having to do half a game without an item you usually get in the first few minutes, working around the lack of that item. (For instance, playing substantial parts of a Zelda game without even a basic sword.)
Some randomizer modes also convert a more linear game into a more open-world game, by making it so you can go anywhere from nearly the beginning, though what you can do in those places will still be limited by the items you have.
Archipelago also supports multiworld with the same game, which I suppose might seem obvious but hadn't occurred to me until I saw multiworld co-op races with the Final Fantasy VI randomizer Worlds Collide -- two teams of two, both teams run the same seed, each player running half of the progression. Requires a lot of thoughtful coordination.
The top priority is picking games you're familiar with; you almost never want to play a randomizer of a game you've never played normally. That does not mean you need to be an expert at the game, but you should probably be able to beat the game with more-or-less 100% completion.
Beyond that, personally I'd suggest Super Metroid or any Zelda game.
Ok but a lot of the games I’m seeing here seem like they would have vastly different schedules. Like Risk of Rain 2. Like is it really feasible to run ocarina of time in parallel with risk of rain 2 given the difference in completion time?
I don't know about that particular game, but some of the games have options to make them quicker, for exactly the reason of making completion times more comparable across games. For instance, some of the supported RPGs have options to multiply experience and money, to reduce grinding, as well as options to shorten or skip long cutscenes, modify victory conditions (e.g. number of MacGuffins required), or add fast-travel systems to games that didn't originally have them.
TLDR context: a randomizer shuffles around game items/skills and even game areas such that the game is completed in a different order. Archipelago shuffles those things among different playthroughs. For example, I might pick up an item in my Pokemon playthrough that unlocks a gun in your Doom playthrough, and when you pick up a keycard it might unlock Ground Pound for a Mario player, and so on. It's like a giant collaborative puzzle game.
Here's an example with 114 playthroughs (includes some game spoilers in the latter half): https://youtu.be/YwUIfxF3ujo
I don't understand this at all. So if you were playing Doom, you might get stuck because someone in some random other game needs to find your key? That sounds awful.
It's intended to be a collaborative endeavor, often played with people who are on a live call with each other. In the kinds of games that work well with randomizers, you usually have multiple different options for how to proceed, and you have to figure out how to check as many item locations as possible to unlock things for yourself and (in the case of Archipelago) for other players.
It doesn't work as well with linear or mostly linear games.
And as another reply noted, sometimes you get stuck ("BKed"). Sometimes each person has more than one game in the randomizer, so they have a couple of options to play further. Sometimes people go watch someone else play until they're unblocked again.
That's definitely a concern. Players call getting stuck by others' checks "BK'd" because a player once went out to get Burger King and returned before they got unwalled. But I think sharing the challenge/frustration and randomness with other players is the fun part, and that's what makes this such an interesting way to play games.
The organizer can also kick inactive players out and release their checks. You could play solo with one or multiple games.
At some point, people started combining games; most notably, "SMZ3" is a two-game randomizer for Super Metroid and Link to the Past (already two very popular games for randomizers), in which you're playing one SNES cartridge that has both games on it and you can step in specific doors to switch from a spot in one game to a spot in the other game.
Archipelago is an evolution of those multi-game randomizers, which combines the logic from each game to ensure that someone is always able to proceed.
And there are options you can choose to make things simpler; for instance, you can prevent certain key items from being very late in the game. But it's also fun to not do that, and end up (say) having to do half a game without an item you usually get in the first few minutes, working around the lack of that item. (For instance, playing substantial parts of a Zelda game without even a basic sword.)
Some randomizer modes also convert a more linear game into a more open-world game, by making it so you can go anywhere from nearly the beginning, though what you can do in those places will still be limited by the items you have.