expression, ichidan verb
fasten a button; button up
Literal action of fastening a button on clothing. The verb 掛ける here means to hook or fasten.
寒いので、コートのボタンを掛けた。
Because it was cold, I buttoned up my coat.
子供はまだうまくボタンを掛けられない。
The child still can't fasten buttons well.
Compound of ボタン (button, from Portuguese botão) + を (object marker) + 掛ける (to hook, fasten). The expression is transparent and literal.