It means to anoint with specially prepared oil (Exodus ch.29). Elsewhere in the Tanakh (Bible) it is also used to mean royalty or a great person (Psalms 105).
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The Torah goes into great detail about the anointment of Aaron as the high priest. Technically, he was a messiah, since the word just means that he was anointed. In this sense, all of the high priests were anointed and therefore technically messiahs. The Torah also warns the Israelites not to raise up a king overthemselves. It does not go into any detail about kings, but later, when Saul was installed as king, he too was anointed and therefore became, technically, a messiah. Once David ascended to the throne, each of the kings in the line of David was, technically, a messiah.
Only later, after the destruction of the first temple and the Babylonian exile, did the idea of restoring the messianic line(s) grow to something of cosmic significance.