Why Does “I’ll Put the Kettle On” Often Mean “Let’s Have a Drink”?

“I’ll put the kettle on” means that the speaker will start boiling water, usually before making tea or coffee. Here, on does not describe placing the kettle on top of something. It means setting it to work; the phrase suits both an electric kettle and one used on a stove.

In everyday Australian and British English, the sentence can also function as an easy act of hospitality: boil the water first, then sit down and talk. It is not a formal invitation, and it does not promise tea rather than coffee.

A: You look frozen. Come in.
B: Thanks.
A: I’ll put the kettle on.

https://dictionary.cambridge.org/dictionary/english/put-the-kettle-on