I thought mana was implicetely mystical, or am I suffering under a misapprehension?
Well, generally in Polynesian culture it is - mana is the energy or force that exists in all things (living and static) and when you have mana, what it really means is you have power or authority over mana. Kinda like being a Jedi.
However in Maori culture is has evolved somewhat, and the two key principles of mana are more earthly:
mana tangata - this is authority derived from whakapapa (geneology). A person who has whakapapa that includes a great deal of mana, will themselves have a great deal of mana.
mana huaanga - this is authority derived from the ownership of possessions that can be used to bind people into agreements - basically it means having resources to trade. (This is why governance over "treasures" (natural resources) was such an issue with the Treaty of Waitangi)
The other way is through prowess in battle.
One of the key distinctions of Maori mana is that it is grounded in more practical application of power, rather than any sort of appeal to spirits. For example there is mana whenua which is recognition of power or authority over land, that a tribe (iwi) may have. However this mana is not a result of some sort of mystical appeal, but rather the result of the tribe actually demonstrating they have authority over the land.
Now, obviously in these early cultures the spiritual pervaded culture, and wasn't really seen as anything distinct from the physical world, so mana, like everything else, had a spiritual component. But given that it was a measure of how much authority could be demonstratively
exercised and how much respect was
given, mana was still very much a real thing. Still
is very much a real thing - mana is still very important in Maori culture, and I have experienced it first hand - my Uncle (Te Pakaka Tawhai - Professor of Maori Studies at Massey University) had a great deal of mana in life, and now that he is dead my cousins carry that mana. It's undeniably there.
ETA.
It should be pointed out, in explanation of this, that the Maori relationship to the spiritual world, and deities, was not one of worship, so appealing to a deity or spiritual concept for power was never going to be very effective if you couldn't demonstrate your ability to actually impose that authority. My Uncle explained the nature of Maori religion quite succinctly in one of his works:
The purpose of religious activity here is to seek to enter the domain of the superbeing and do violence with impunity: to enter the forest and do some milling for building purposes, to husband the plant and then to dig up the tubers to feed one's guests. Thus that activity neither reaches for redemption and salvation, nor conveys messages of praise and thanksgiving, but seeks permission and offers placation.
Tawhai, P. 1988
So while mana (and the accompanying
tapu) had a mythological and religious status, it was grounded in social practicality.