Two things happen. The first is that the bales heat up - can get quite hot, even catch fire. Push your arm in amongst the bales to check for heat. The heat promotes rot which gives you mouldy hay. Mouldy hay gives you famers lung and is unpalateable for animals.
If it truly is wet still and your forecast is for a couple of scorching days, you could unwrap it all, spread it again and re-bale, but it's an awful faff if the hay is only slightly damp in patches. Only you know what it's like.
It could be that a couple of days stooked up in the sun will be enough to air the bales.
We have no days forecast without some rain for the next week, so we are nursing our crop through and hopefully we will get it some time
It is so difficult to decide which risks to take when making hay. No wonder most folk round here go for haylage and silage.