Clitoria Ternatea is one of four herbs traditionally used as Shanka Pushpi, an Ayurvedic medicine used to promote neurological health. It shows promise in animal models for its memory enhancing effects, and has a wide spectrum of neurological benefits (anti-depression, anxiolytic, anti-pyretic) yet for these latter claims preliminary evidence suggests it isn't overly potent.
Some other preliminary evidence suggests that it might be healthy for the liver and circulating lipoproteins, as well as a possible benefit diabetics by inhibiting glucose uptake from the diet. However, these claims are much too early to guess their practical relevance on.
Toxicological studies on rodents and historical usage (partially confounded with the three other herbs) suggest that Clitoria Ternatea is safe, but limited evidence exists currently.