Origins
The word 'vocal' sits at the center of one of the largest and most important word families in English — the family of the voice. From the same Latin root that produced 'vocal' come words for calling, speaking, naming, and summoning, spanning religion, law, music, and everyday speech.
English adopted 'vocal' in the late fourteenth century from Latin 'vōcālis' (sounding, speaking, of the voice), an adjective formed from 'vōx' (voice, sound, word, genitive 'vōcis'), from PIE *wekʷ- (to speak, to voice). The adjective originally described anything pertaining to the voice or produced by the voice. Its figurative sense of 'outspoken, inclined to express opinions freely' developed later, by the seventeenth century.
Latin 'vōx' and its verb form 'vocāre' (to call, to name, to summon) produced an extraordinary range of English words. 'Voice' entered English from Old French 'voiz,' from Latin 'vōx.' 'Vowel' comes from Old French 'vouel,' from Latin 'vōcālis littera' — a 'voiced letter,' one pronounced with the vocal tract open. 'Vocabulary' comes from Medieval Latin 'vocābulārium,' from 'vocābulum' (a name, a word — something you call things by). Each of these preserves a different aspect of the voice: its quality, its phonetic character, and its naming function.
Word Formation
From 'vocāre' (to call) come the great compound verbs. 'Invoke' (to call upon — for aid or authority). 'Evoke' (to call out — to summon a memory or response). 'Provoke' (to call forth — originally to challenge, then to anger). 'Revoke' (to call back — to withdraw or cancel). 'Convoke' (to call together — to assemble). 'Equivocate' (to call equally — to speak ambiguously, using words that could mean two things). 'Advocate' (from 'advocātus,' one called to speak for another — a legal defender). Each prefix redirects the basic act of calling.
'Vocation' — a calling — deserves special attention in this family. Latin 'vocātiō' meant 'a calling, a summons,' and in early Christian usage, it acquired the specific sense of God's call to a religious life. From this came the English distinction between a 'vocation' (one's true calling, often with spiritual overtones) and a mere 'occupation' (what one happens to do). The related 'avocation' (from 'āvocātiō,' a calling away) originally meant a distraction from one's vocation — a hobby or side pursuit.
The Greek cognate of PIE *wekʷ- is 'epos' (word, song, narrative), which gave English 'epic' (a grand narrative in verse — originally an oral recitation) and 'epopee' (epic poetry). The connection between Latin 'vōx' (voice) and Greek 'epos' (word, narrative) shows how the PIE root branched: in Latin, it became the physical voice and the act of calling; in Greek, it became the poetic word and the act of narrating.
Figurative Development
In music, 'vocal' refers to singing as distinct from instrumental performance. 'Vocals' as a noun (the sung parts of a song) is a twentieth-century usage that has become ubiquitous in popular music terminology. A 'vocalist' is a singer. 'Vocal cords' (or more accurately, 'vocal folds') are the vibrating tissues in the larynx that produce voice — the physical organs that make the entire metaphorical family possible. The word 'vocal' thus spans the full range from the anatomical to the figurative, from the folds in your throat to the opinions you insist on expressing.