Where does the concept of "Mana" as a resource come from?
Solution 1:
It's almost certainly derived from a pan-Polynesian idea of "that which makes something effective" - usually, what makes magic effective. "Mana" tends to travel in the company of the idea of "taboo", the complex of rules that distinguish something as sacred. Mana comes from obedience of taboo, from the performance of certain rites, from pleasing the spirits of ancestors, or from other sources, depending on the particular island whose mana/taboo complex you're studying. (Keesing's Kwaio Religion is probably the most readable account, and recommended reading - the Kwaio have a verb that's a cognate of "mana", and their practices revolve around satisfying ancestor spirits who can in turn "namana"-ize their descendants' activities, mundane and magical alike, so that they meet with success.)
Larry Niven is probably the writer who brought the idea into Western fantasy literature, as the Wikipedia article indicates, and it spread in that millieu during the 1970s.
Solution 2:
The word Manna exists as far back as Hebrew, first seen in the book of Exodus referring to the food that God produced out of nothing to feed His people. As Colin Creitz points out, the word Mana exists in the Austronesian family. However, the Hebrew Manna may in fact originate as a word play on the Aramaic 'Mann hu' meaning 'what is it?' and the ancient Egyptian word 'Mennhu' meaning food. The suggested meaning is that 'Manna' is an inscrutable gift from God (a dew found 6 mornings a week in the desert with the taste of honey)
Later references to Manna come in Roman Catholic lore as a fluid constantly exuding from the tomb of Saint Nicholas. It is also suggested by some Christians that God intended us to be vegetarian and cite the existence of Manna as proof.
From the late 14th century, Manna was known as a spiritual nourishment to scholars. The word Manna appears in close proximity to Merlin in Henry Lovelich's story Merlin. I don't know exactly when that came out, but its in proper old English, so I suspect it is old.
Solution 3:
First time I heard of it was in Dungeon Master on Atari (1987), one of the three resources (health, stamina,mana)
EDIT: prior to Populous 1989.
Solution 4:
"Hawaiians and other Polynesians believed that their kings and queens had a concentrated sacred energy called mana, which common people could not share. To maintain this sacred energy, the rule for a king was that his most appropriate wife was his sister. This set of cultural beliefs illustrates the manifest function of royal endogamy"
Found this while studying for my anthropology exams.
Solution 5:
Not neccesarily a real reason for this, but this piece of mythology bears a strong resemblance to the way that magic is used in current fantasy fiction.
Finnic mythology also has a concept of "mana". First it was "Maan ala", meaning a place underground. Then this name evolved shorter, turning into Manala. But finnic languages have the property of suffixes adding additional meanings. And "-la" is usually used to turn non-locations into location names. Usually it can denote someone's place of living. So, it was only an unescapable conclusion that Manala is the place where Mana lives.
Mana then evolved to mean the ruling spirit of the otherword(place where the dead go). Then the word "mana" evolved to mean stuff, which must have otherworldy origin. For example extraordinary deeds - shaman performing a ritual(to mana(action)), a person winning a fight of extraordinary odds(mana is strong in him or he has lots of mana(desciptive)), a person being with exceptionally good personality(hes like a child of Manala(descriptive)).