Moringa oleifera is a tree that is sometimes called the Tree of Life or a Miracle Tree, but rather than this being in reference to its potential medicinal usage this is actually refering to how it is a very valuable food crop (it is drought resistant, grows very fast, and is highly nutritive) and even beyond food it serves many benefits in third world countries such as having an ability to be used for some crafts (due to being a tree) and cleaning water.
For usage as a supplement, moringa oleifera is recommended mostly as being a highly nutritious antioxidant. While it is indeed nutritious, supplemental dosages are too low to acquire adequate nutrition from and this claim is not relevant; it is a relatively potent antioxidant, and while it seems to be less potent than other herbs when tested outside of a living system it does appear to be quite potent when tested in living models. The reason for the increased potency in living models is not known (although it is possible that it can induce cellular transcriptional changes similar to sulforaphane since the bioactives are similar in structure), but the antioxidant properties seem to underlie the vast majority of benefits associated with this supplement.
There are also antiinflammatory effects that, while less studied, seem to be quite effective. One of the bioactives, RBITC, is effective in suppressing macrophage activation in the nanomolar range and is worth some future research into. Beyond that, there does appear to be a nice anti-diabetic effect that has undergone preliminary human testing. This work suggested that this moringa oleifera may promote pancreatic health and reduce blood glucose secondary to this.
While both the antioxidant and antiinflammatory properties are somewhat interesting, until the exact mechanisms and relative potency to some other antioxidants or antiinflammatories are tested it is hard to recommend this supplement over other options.
It is important to note that although the plant is generally considered to be 'nontoxic', this does not appear to be the case at all times. While supplemental dosages listed below appear to be safe from all tested toxicity a, relatively small increase (3-4 times the recommended does) is known to cause genotoxic damage and may promote cancer formation whereas higher doses cause overt organ damage (mostly liver and kidneys). This effect is seen with the seeds while toxicity of the leaves seems to be a lesser concern. Beyond that, reasonable supplemental dosages appear to be able to induce abortions in pregnant rats and thus supplementation is contraindicated (not advised) in pregnant women.