Being FDA approved doesn't mean that it will be good for you. It just means it met their criteria for health & safety. But this doesn't mean that "bad" or "unsafe" things don't make it through the system and affect your health, as with the BPA scares in cans & packaging. Some merchants can also say their product is FDA approved when it's not. The chinese for example are well-known for producing frauds & counterfeits, along with products that are simply just contaminated, so if you buy from dodgy third-party websites or an online marketplace like amazon or ebay, be cautious so that you get a legitimate product.
This quote basically sums up how they make their decisions:
"FDA does not develop or test products before approving them. Instead, FDA experts review the results of laboratory, animal, and human clinical testing done by manufacturers. If FDA grants an approval, it means the agency has determined that the benefits of the product outweigh the known risks for the intended use."
https://www.fda.gov/ForConsumers/Consum ... 047470.htm
In other words, the FDA doesn't do any testing. The manufacturer does the tests on their products, submits the results to the FDA and some nameless bureaucrat there decides that if it seems legit or it's "worth the risks", then it gets approved.
On the whole, I'd say it's trustworthy, but as with anything else you shouldn't place your trust blindly.
So what are you wondering about, specifically?