Tree radical on the left — 桃 names both the fruit and the tree. Anchors 桃 in the family of fruit-tree characters alongside 梨 (pear), 李 (plum), 杏 (apricot), 桂 (osmanthus). Tells the reader instantly: this is a tree-fruit.
Right component supplies the sound: 兆 zhào → táo with regular initial drift (Old Chinese had a complex initial that split between Mandarin zh- and t-). Same phonetic in 跳 (jump), 挑 (select), 逃 (flee) — the tao/tiao family clusters around 兆.
In Pop Culture
蟠桃Pántáo
Peaches of Immortality
Heavenly peaches Monkey King stole in Journey to the West.