It is known as 'private labeling' - essentially, you make the product which they will sell as their own brand. It is a very common method of production, you would be surprised how many products are sold under one label but made by another.
The best advice I can give you is to ensure you lock them in and do not give them the recipe. The reason they will private label is that they either do not have the resource (people/equipment) or the skill to do it themselves, and if it is your specialty, then they figure it will be cheaper in the long run for them to buy from you.
If you already wholesale, it is just the same - except they may provide you with packaging to use as well. Just ensure they do not have 'made by <their name>' on the label, but maybe 'made for <their name>' instead. But don't expect to get your brand on there.
Some people do not like to private label for others, I think it is a terrific way to increase your revenue.
One of my brands on the shelves in my store is private labeled, I get the product, made to my recipe, delivered in bulk and we repackage.
Hope this helps
It's THEIR recipe and it's you that does not know what it is. However working it out is not really too hard.
Simply tasting will tell many people what the receipe is. I can pretty much do that with many products. I also used to work in a laboratory where we used to grab competitor products and "backwards engineer" them. In essence take them apart and measure them physically and chemically.