It means you have Salmonella.
Mayo is made from eggs. Salmonella is normal flora to the genitourinary tract of chickens -- all eggs are colonized with salmonella on the outside. All industrial food processes that use eggs require pasteurization or treatment to decrease the risk of salmonella transmission.
Pasteurization doesn't kill everything. There can still be weakened bacteria living in there. Just like pasteurized milk, it's fine as long as it stays cold enough to keep those bacteria from reproducing, but if it gets warm enough, they can grow like wildfire. Even when kept cold, some bacteria can still grow slowly. That's why it has an expiration date and must be kept refrigerated.
By leaving it out, those salmonella bacteria had a perfect environment in which to grow like crazy. And they did. And you ate them.
The good news is, salmonella is easy to treat. Stay hydrated and rest and it will pass in a few days, but your best bet is to see your doctor. Significant diarrhea and vomiting can lead to electrolyte imbalances and the infection can also allow other bacteria that aren't normally a problem to overgrow. They may want to set you up with a course of antibiotics.
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