Magic, at its core, is about spirituality and enlightenment. There are certainly aspects intended to help heal, provide short cuts to success, and wealth, and so forth, but most of this has to do with a mixture of psychology as well as any real magical effect.
Various healing methods utilizing magic, energy, etc. have been shown to help -some- people scientifically, but the results are varied enough that it is quite easy to be skeptical about it.
Many other forms of magical practice, such as astral projection, or evocation (the conjuration of spirits) is also rather difficult to prove, as much of it stems from unverified personal gnosis - or experiences that can't be verified scientifically, and are often experienced only by one person.
There isn't a lot of flash and flare to the whole thing, and in the end, it's largely about personal experiences as I've said. Proof comes from exploring enough to have other people experience the same things you did, or otherwise setting up controls to help you determine if the same results could have happened without any "magical" effort while all other conditions are the same. Otherwise, people tend to just believe what they wish and take comfort in it, much like many other practices of spirituality. Often it is ridiculous, often it can -seem- ridiculous, but in the end, if people find comfort in it or the means to improve themselves mentally, emotionally, or in any other such way... why not?