Colloquial and a bit playful, what kids would say. The plain medical/neutral form is 肚脐 (dùqí) without 眼; the suffix 眼 ('hole, eye') makes it more visual and conversational. In Beijing speech you'll often hear it with -er: 肚脐眼儿 (dùqíyǎnr).
memory
Compound logic: 肚 (belly) + 脐 (navel/umbilicus) + 眼 (hole), 'the hole at the belly's navel.' Each piece carries meaning, so the word is fully transparent once you know the parts.