An unstressed syllable is the part of the word that you don't emphasize or accent, like the to- in today, or the -day in Sunday. An unstressed person is someone for whom every day feels like Sunday.
When you pronounce a word with multiple syllables, like avocado (to choose a random example), you put more pressure on some syllables than others — in this case, the ah and the cah. Consider those syllables stressed. If they were people, they'd be biting their nails and pulling out their hair while sitting at a desk piled with paperwork. The vo and the do, on the other hand, would be unstressed — lounging with their feet on the desk, doing crossword puzzles.
adj not bearing a stress or accent
(music or poetry) ending on an unaccented beat or syllable
light, unaccented, weak
(used of vowels or syllables) pronounced with little or no stress