飲 is to drink, and 品 is item, so 飲品 is drink items.
Ordering
杯 is cup (or mug or glass) and is the measure word for water (and other drinks), and 一 means one, so, for example, to order a glass of water, ask for 一杯水 (yāt būi séui in Cantonese, yī bēi shuǐ in Mandarin), one cup of water.