My question is what does this money mean exactly?
The prélèvement à la source is just a provision you pay ahead of time for taxes you may or may not actually owe. How much you owe can only be determined after the year has ended and you submit your tax return. Like all pay-as-you-earn systems, the withholding rate is based on assumptions. The tax office and your employer have no way to know about charitable donations, other sources of income, etc. until you submit your tax return.
On top of that, for historical and cultural reasons the French tax office actually shares less information with your employer than the tax office in many other countries. It's also not very good at estimating your future tax rate based on the information it does have. So the taxes withheld from your account are really just a rough estimate.
One of the most important assumption in your case is that the rate you paid is based on your monthly salary multiplied by 12. So I suspect it might not have properly accounted for your income (or lack of income) between January and August 2022. In France, the first €10k of your income are tax-free and the next €17k are taxed at 11% (for someone filing alone).
Another issue is your family situation. If you have a spouse and kids and if your spouse also has an income, this can have a significant impact on your income tax. Usually, the tax office does know about that and can take it into account to calculate the withholding rate but if your situation changed during the year or you are a new taxpayer, they may only learn about it when you file your tax return.
Do I have to pay it back in 2024? How does this work?
No, this amount is final (outside of fraud and appeals). The tax return you file in the spring and the document you receive during the summer (“avis d'imposition”) are still the most important thing. Everything else (and especially the tax rate and payments you are making now, for 2023) is provisional.
Note that it can work both ways. For example if you get a salary raise or some sort of windfall income and you do not actively update your tax rate, you might end up paying too little. Also make sure your withholding rate won't be lowered based on your 2022 tax return as that would mean having to pay extra some time down the line.