Tama is Japanese for the spirit or soul of a human (kanji: either 魂 or 霊). They are one of the central aspects of the spiritual landscape of Shinto, but unlike the kami (nature spirits) and oni (demons), tama are comparatively ignored in Western adaptations of Japanese culture... in fact, the word appears most often as a character name for comparatively minor anime and manga characters. The most famous tama in the Western world, by far, is the Shikon no Tama (Jewel of the Four Souls), a powerful jewel in the InuYasha series.
Part of this is simply because, ideally, one does not leave behind a tama when they die, but a mitama, literally, an honorable soul (confusingly, mitama can also be used to refer to the spirit of a kami). A tama is traditionally seen as an outside force that inhabits a human during their lifetime, to leave again when they die. The honorific mi is appropriate for showing respect for those you knew while they were alive.
But perhaps you heard tama used in another context. The spoken word tama is actually a collection of homophones, each with a different kanji; e.g., 魂 means 'soul'; 球 means 'sphere'; 玉 means 'ball'; 弾 means 'bullet'. Japanese is just as complex as English, and me understanding what's going on in Japanese wordplay is simply not going to happen. However, I should mention that tama can also be pronounced tamashii, which probably originally meant something like 'the task of a tama', but is now treated as a synonym. This allows for fun things like an Xbox 360 game named Tama Tamashii, literally, 'Bullet Soul'.
mauler adds: "In isolation, this word is almost always pronounced tamashii. My sense of the difference is that tamashii means 'spirit' in the more abstract sense as in 'the Japanese spirit' or a person's immortal soul, whereas tama is more concrete, like in a tree spirit or a fire spirit. Tama are a concrete manifestation of kami."