Here's a breakdown:
* Poly- means "many"
* Syllable is a unit of pronunciation consisting of a single vowel sound, with or without surrounding consonants.
So, a polysyllabic word has multiple vowel sounds within it. For example:
* "Elephant" has three syllables (el-e-phant)
* "Beautiful" has four syllables (beau-ti-ful)
* "Supercalifragilisticexpialidocious" has 18 syllables (you get the idea!)
Polysyllabic words are often considered more formal or complex than shorter, simpler words.