Transpilation means compiling to a source code in another language. In case of Elm, it gets compiled to a JavaScript source code, which you then run in your browser.
The other logos in that slide:
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Babel: newer/experimental version of JS into “old JS”, essentially adding support for new features
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TypeScript: typed JS into JS
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ClojureScript: Clojure into JS
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Reason: Reason into JS (through the intermediate step of OCaml, I think?)
- I don’t know what the last logo is for
Related: Language Graph - allows you to find a chain of such transpilers from language A to language B, if it exists.