Primary means basically "first." When you vote in a primary, that is the first election in a series. When a matter is of primary concern, it means it's of first importance. Primary school is the first you go to (after nursery school, at least).

There's an interesting alternate system for counting first, second, third, etc. up to tenth. It's primary, secondary, tertiary, quaternary, quinary, senary, septenary, octonary, nonary, and denary. There's also a word for twelfth, duodenary, though that — along with all the words after tertiary — is rarely used.

Definitions of primary
  1. adjective
    of first rank or importance or value; direct and immediate rather than secondary
    primary goals”
    “a primary effect”
    primary sources”
    “a primary interest”
    basic and fundamental
    preceding all others in time or space or degree
    being or productive of something fresh and unusual; or being as first made or thought of
    of primary importance
    being an immediate result or consequence
    received directly from a source
    being a regular member of a team
    (of e.g. information) not secondhand or by way of something intermediary
    particular, special
    first and most important
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    being of second rank or importance or value; not direct or immediate
    inessential, unessential
    not basic or fundamental
    not original; not being or productive of something fresh and unusual
    alternate, alternative, substitute
    serving or used in place of another
    auxiliary, subsidiary, supplemental, supplementary
    functioning in a supporting capacity
    accompanying; concomitant
    not as a direct effect or consequence
    derived from what is primary or original; not firsthand
    being a replacement or substitute for a regular member of a team
    ready for emergency use
    derived from what is primary or original by two intermediate steps
    (of a stream) flowing into a larger stream
    substitute, utility
    capable of substituting in any of several positions on a team
    experienced at secondhand
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  2. adjective
    of primary importance
    synonyms: basal
    basic and fundamental
  3. adjective
    most important
    “policemen were primary targets”
    synonyms: chief, main, master, principal
    important, of import
    of great significance or value
  4. adjective
    of or being the essential or basic part
    synonyms: elemental, elementary
    pertaining to or constituting a base or basis
  5. adjective
    not derived from or reducible to something else; basic
    “a primary instinct”
    not derived; primary or simple
  6. noun
    a preliminary election where delegates or nominees are chosen
    synonyms: primary election
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    direct primary
    a primary where voters directly select the candidates who will run for office
    closed primary
    a primary in which only registered members of a particular political party can vote
    open primary
    a primary in which any registered voter can vote (but must vote for candidates of only one party)
    type of:
    a vote to select the winner of a position or political office
  7. noun
    one of the main flight feathers projecting along the outer edge of a bird's wing
    synonyms: primary feather, primary quill
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    type of:
    flight feather, pinion, quill, quill feather
    any of the larger wing or tail feathers of a bird
  8. noun
    (astronomy) a celestial body (especially a star) relative to other objects in orbit around it
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    type of:
    celestial body, heavenly body
    a natural object visible in the sky
  9. noun
    coil forming the part of an electrical circuit such that changing current in it induces a current in a neighboring circuit
    “current through the primary coil induces current in the secondary coil”
    synonyms: primary coil, primary winding
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    type of:
    reactor consisting of a spiral of insulated wire that introduces inductance into a circuit
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