The best thing to understand what are these providers is to look at nice example.

Do you like blocks? I know you do.

Let's create a class I would name MModdingExampleBlocks here, but you can name it however you want. Just don't forget to also change this reference at every place I use it in the code.

public class MModdingExampleBlocks {

	public static void register(AdvancedMod mod) {
	}
}

That class will contain content. Then we must provide. You know what that means? fish Content providers!

Whereas you can name MModdingExampleBlocks#register (both the class and the method) however you want, the method must be public, static, return nothing and must pass an AdvancedMod object as the unique argument.

Let's give it to our manager in the initializer!

public class MModdingExampleMod implements ExtendedModInitializer {

	public void setupManager(ElementsManager manager) {
		manager.content(MModdingExampleBlocks::register);
	}

	// ...
}

You might think, where are we using ContentProvider? Well, actually, MModdingExampleBlocks::register is a ContentProvider object. This is because ContentProvider is a functional interface. If you do not know what is a function interface yet, do not worry. You're coding in java. They will beat your ass up. You'll end up understanding them.

Let's create a very simple Block and its resource key.

public class MModdingExampleBlocks {

	public static final ResourceKey<Block> EXAMPLE_BLOCK_KEY = MModdingExampleMod.createKey(Registries.BLOCK, "example_block");

	public static final Block EXAMPLE_BLOCK = new Block(BlockBehavior.Properties.of().setId(EXAMPLE_BLOCK_KEY));

	public static void register(AdvancedContainer mod) {
	    mod.register(BuiltinRegistries.BLOCK, "example_block", EXAMPLE_BLOCK);
	}
}

If you followed every step correctly, the content is provided when you launch the Development Minecraft Instance. You should have your very archaic simple block in game!