To put down is to place something on a surface. Also, quite differently, to insult somebody.
The physical sense is plain, and putting a book down is the opposite of picking it up. The insulting sense is where the noun a put-down comes from, meaning a remark designed to make somebody feel small. There are three more: putting down a deposit means paying it, putting down an animal means having it destroyed, and putting somebody down as something means judging them to be it.
put-down Deverbal from put down.
Etymology from Wiktionary, CC BY-SA