Hesperidin is a compound in orange peels that gives the flavonoid hesperitin to the body, and this flavonoid mediates most benefits of hesperidin including an increase in circulation and possible brain protective effects. Hesperidin, alongside naringenin, are known as the main citrus flavonoids.
Hesperidin is a bioflavonoid glycoside commonly found in citrus fruits (most notoriously oranges) and is a sugar-bound form of the flavonoid hesperitin. Hesperitin is known to mediate the actions of hesperidin in the body, and since hesperidin needs to progress to the colon to be ‘released’ by intestinal bacteria it acts as a time-release for hesperitin; one serving of hesperidin seems to increased blood levels for over the course of a day or so when consumed in this manner.
If we are to look currently at the human evidence on orally ingested hesperidin, it appears to promote blood flow (minorly to moderately) and may have a weak influence on blood pressure while it is pretty much ineffective on cholesterol and triglycerides. Not much other human evidence exists aside from the cardiovascular parameters mentioned above, and it seems pretty weak at improving parameters of diabetes as well (with exception to the eyes, diabetic retinopathy, as preliminary evidence suggests that hesperidin is quite protective of them).
That being said, in animal studies oral intake of hesperidin at a dose similar to that used in humans seems to be a very potent cardioprotection agent and is quite protective of the brain in response to various stressors; the protection is antioxidative in nature, but it seems to work through a currently not identified antioxidant responses from the genome. Aside from the protective effects (most notable in the heart and brain, but extend to every organ), hesperidin may be able to reduce a lack of appetite and have minor anti-allergic properties.
Orange peels can actually be used to get the supplemental dosage of hesperidin seen in the human studies. Dr. Brant Cortright suggests the following Bioflavonoids (Quercitin, Hesperidin, Apigenin, Diosmin) which encourages Neurogenesis or the formation of new brain cells.