盘 doubles as a measure word: 一盘菜 (a plate/dish of food), 一盘棋 (a game of chess), 一盘录像带 (a videotape). The measure word usage comes from things arranged on or wound around a flat surface.
culture
算盘 (suànpán, abacus) literally means 'counting tray.' The Chinese abacus was used for centuries and is still taught to children as a mental math technique (珠心算, zhū xīn suàn).
Bottom vessel radical - the indexing semantic. Pictures a wide footed bowl seen from the side, two vertical legs and a flat horizontal base. Marks 盘 as a shallow open dish or tray. Other vessel-radical words: 盆 (basin), 盖 (lid), 盐 (salt-tray to salt), 盗 (drink-from-vessel to steal).
Top 舟 - pictures a boat seen from the side, with planks and a ridge. In 盘 it stands in for the original phonetic 般 (sort/kind), which the simplified form has shortened to just its left half 舟. Supplies the sound bān to pán, a regular Mandarin shift.