Red sea salt is just one of a variety of exotic salts being touted as a more natural and therefore healthier alternative to standard table salt.
Iodine
Sea salts are less processed than regular table salts, and as a result contain the remains of microscopic sea life. This gives them iodine, a necessary element missing from many common salts.
Minerals
The most common red sea salts come from Hawaii and the Himalayas. Their red color comes from volcanic matter and extra iron, reputedly imbuing them with additional minerals not found elsewhere.
Warning
While many blogs and retailers tout the enhanced healthiness of these salts, there is virtually no documented evidence that this is the case.
Conclusion
Given the lack of support from the mainstream medicinal and nutritional communities, it's difficult to determine whether red sea salt provides any additional health benefits beyond those commonly attributed to sea salt in general.
Fun Fact
Red sea salt is recommended more often as a colorful garnish or finishing seasoning than it is a true health supplement.