Alliteration is the repetition of the same initial consonant sound across two or more neighboring words or stressed syllables — wild and woolly, threatening throngs.
It is a device of sound, not of spelling. Kind and cat alliterate because both open on a hard /k/; kind and knight do not, despite the shared letter, because the ear governs and the k in knight is silent. The effect binds a phrase into a single unit of memory, which is why alliteration survives wherever a line has to be recalled without being reread: proverbs (busy as a bee), tongue twisters, headlines, band names, and brands. Old English verse was built on it structurally — Beowulf organizes each line around repeated initial sounds rather than end rhyme, a system that predates rhyme in English poetry by centuries.
The word is a Latin coinage of the 1650s, from Modern Latin alliterationem, a noun of action from alliterare, "to begin with the same letter," from ad ("to") and littera ("letter"). The name describes the device by its letters even though the device works on sounds — the mismatch that trips up most first attempts to identify it.
Two neighbors mark its edges. Assonance repeats vowel sounds inside words; consonance repeats consonant sounds anywhere in them, often at the end. Alliteration is specifically initial. It also differs from a 📝portmanteau, which fuses two words into one new word: alliteration leaves every word intact and does all its work on the ear.
I have found that the allure of alliterations can be brilliant for branding. They have a tendency to stick in one's skull such that they are magic for marketing. However, it seems that forcing a fit, as has been exemplified in this explanation, tends to have the opposite effect. Use responsibly. Favorites of mine: 📝Artful Advocacy, 📝Strategically Shitty, and 📝Tipsy Tours.