What does an arrow ("->") symbol mean on the command line?

In the MySQL command-line tool that means the tool expects your input to continue on the next line. Here it is waiting for the destination path.

Common "full" SQL commands are written with indents, which is supported at the command line. You would say something like

SELECT
    `users`.*
FROM
    `users`
WHERE
    `users`.`is_active` = 1 AND
    `users`.`age` < 13
ORDER BY
    `users`.`username`

The arrows are an interactive continuation prompt. If you enter an unfinished command, the SQL shell (invoked by the mysql command) is waiting for the rest of it.

In this particular case, the SQL shell is waiting for a destination path for the mysqldump.

Also, commands aren't complete until you terminate commands with a semicolon. (Thanks @MrStatic)

You do indeed have a syntax error; SQL commands must end with a semicolon. For example:

mysqldump my_database;