[elisp] not clear why <let> uses 2 pairs of "( )"

When command "let" is introduced it is not really explained why it evals through double parenthesis:

> ;; You can bind a value to a local variable with `let':
> (let ((local-name "you"))
> (switch-to-buffer-other-window "*test*")
> (erase-buffer)
> (hello local-name)
> (other-window 1))

Search the repository for the quoted `let` example and read the surrounding Emacs Lisp documentation. Add a concise explanation of why the example uses two pairs of parentheses, and consider the issue complete when a reader can understand that syntax from the introduction alone.

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