What to use for creating embeddable content?

I want to use/create an simple embeddable component system so that any external party that can edit the HTML of their web content can include some content from mine.

Can I provide a simple <script></script> piece of code so that someone else can embed content from my website automatically by embedding the provided script?

We often see that for embedding polls, Twitter posts, etc. into other webpages, I'd like to use something similar.