Red Clover Extract (RCE) refers to any extract that is taken from the red clover plant, known botanically as trifolium pratense which is a good natural source of isoflavone molecules. There are a few brand name products of RCE (Promensil, Menoflavon, etc.) which isolate the isoflavones that are thought to be bioactive, and this mainly refers to two of the soy isoflavones which are also found in this plant (genistein and daidzein) and two structurally similar methylated isoflavones known as biochanin A and formononetin. Specifically, biochanin A is just methylated genistein (and can produce genistein in the body when it is ingested) whereas formononetin is methylated daidzein (can also produce daidzein in the body after ingestion). RCE, and its brand name products, are recommended for the treatment of menopause or asthmatic symptoms.
When looking at research on RCE and menopausal symptoms, there are indeed benefits in isolated studies relative to placebo but there are also many failures indicating that supplementation is pretty unreliable in benefitting symptoms; this may be in part due to differences in absorption or simply due to potential industry bias (since many studies using the brand name products are partially funded by the producers of the products, and the independent studies tend to be more likely to report no significant benefit). There may be a minor reduction in anxiety however, which would be a percievable benefit and needs to be further evaluated. It should also be noted that most studies do reported great benefit with supplementation, but the placebo effect per se is very prominent in studies on menopausal symptoms (case in point, studies on black cohosh where the placebo effect sometimes halves symptoms of menopause alone).
Beyond the above possible anxiolytic property of red clover that needs to be investigated further and a possibly benefit to asthma and cough (also needs to be investigated further), there does not appear to be any significant benefit associated with red clover extract.