Many, multiple
Multi- comes from Latin "multus" (many, much) and signals plurality or multiplicity in a broad sense: multiply = make more of something; multicultural = of many cultures; multilingual = speaking multiple languages; multimedia = using multiple media; multitask = performing multiple tasks simultaneously. Unlike poly- (Greek), multi- comes from Latin.
Multi- vs poly-
Multi- and poly- mean the same thing (many/multiple) but come from different roots: multi- from Latin, poly- from Greek. In formal science, poly- is typically preferred (polymer, polyphony). In corporate and technology language, multi- tends to dominate: multitasking, multimedia, multiplatform, multilevel. The difference is one of register and field, not meaning.