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 increase blood levels for over the course of a day or so when consumed in this manner.
If we are to look at the human evidence on orally ingested hesperidin, it appears to promote blood flow (minorly to moderately) although it's unclear if it has a notable influence on blood pressure; the current research isn't supportive overall, though it hasn't been studied in severe hypertension yet. It is pretty much ineffective for cholesterol and triglycerides from the available evidence. 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, and hesperidin is known to interact with a variety of drug metabolizing enzymes so it should be approached cautiously if also using pharmaceuticals.