means a short, catchy tune or rhyme, often used in advertising, or the light ringing sound made by small metal objects knocking together.

from Almost certainly imitative — an English word born to mimic the sound itself, the tinkling clink of coins or bells, first appearing in late Middle English. The advertising sense (a catchy musical tag) is a much later extension, riding in on radio and television in the 20th century, where a tune that 'jingled' in the ear became the marketer's dream.