Ancient wisdom is not scientific, and it might even be false, but the benefits are very real, and these benefits sort of works to make the wisdom true.
The best example I can give is placebo, the belief that something is true helps make it true, so even if it's not true, you get the benefits of it being true. The special trait ancient wisdom has is this: The outcome is influenced by your belief in the outcome. This tends to be true for psychological things, and advice like "Belief can move mountains" is entirely true in the psychological realm. But scientific people, who deal with reality, tend to reject all of this and consider it as nonsense, as the problems they're used to aren't influenced by belief.
Another case in which belief matters includes treating things with weight/respect/sacredness/divinity. These things are just human constructs, but they have very real benefits. Of course, you can be an obnoxious atheist and break these illusions all you want, but the consequences of doing this will be nihilism. Why? Because treating things as if they have weight is what gives them weight, and nihilism is basically the lack of perceived weight. There's nothing objectively valid about filial piety, but it does have benefits, and acting as if it's something special makes it so.
Ancient wisdom often gets the conclusions right, but get the explanations wrong, and this is likely in order to make people take the conclusions seriously. Meditation has been shown to be good for you. Are you feeling "Ki" or does your body just feel warm when you concentrate on it? Do you become "one with everything" or does your perception just discard duality for a moment? Do you "meet god" or do you merely experience a peace of mind as you let go of resistance? The true answer is the boring one, but the fantastical explanation helps make these ideas more contagious, and it's likely that the false explanations have stuck around because they're stronger memetically.
Ancient wisdom has one advantage that modern science does not: It can deal with things which are beyond our understanding. The opposite is dangerous: If you reject something just because you don't understand why it might be good (or because the people who like it aren't intellectual enough to defend it), then you're being rational in the map rather than in the territory. Maybe the thing you're dismissing is actually good for reasons that we won't understand for another 20 years.
You can compare this with money, money is "real but not real" in a similar way. And this all generalizes far beyond my examples, but the main benefits are found, like I said, in everything human (psychological and spiritual) and in areas in which the consensus has an incomplete map. I belive that nature has its own intelligence in a way, and that we tend to underestimate it.
Edit: Downvotes came fast. Surely I wrote enough that I've made it very easy to attack my position? This topic is interesting and holds a lot of utility, so feel free to reply.
I would tend to give particular credence to any practice which pre-dates the printing press.
The reason is fairly straightforward. Spreading ideas was significantly more expensive, and often could only occur to the extent that holding the ideas made the carriers better adapted to their environments.
As the cost to spread an idea has become cheaper, humans can unfortunately afford to spread a great deal more pleasant (feel free to substitute reward hacking for pleasant) junk.
That doesn't mean failing to examine the ideas critically, but there are more than a few ideas that I once doubted the wisdom of, which made a great deal more sense from this perspective.
As for the particular practice of meditation that you reference, I tend to view spiritual practices as somewhat difficult to analyze for this purpose, as the entire structure of the religion was what was transmitted, not only the particularly adaptive information. To use DNA as an analogy, it's difficult to tell, which portions are of particularly high utility, analogous to the A, C, G, and T in DNA, and which serve as the sugar-phosphate backbone. Potentially useful in maintenance of the structure as a whole, but perhaps not of particular use when translated outside that context.
Which portions of Buddhism are which, I couldn't tell you, I lack practice in the meditation methods mentioned, and lack deeper familiarity with the relevant social and historical context.