But we can't actually elect anybody, can we?
No, we can't. This is what we call parallel voting: the intention is to allow people to experience the political issues of other countries and to express their views on those issues. If the result is striking enough, it certainly achieves an impact: not as immediate or as decisive an impact as electing a President or Prime Minister, but an impact nonetheless.
Luckily, in the modern world, influence comes in many forms. The aim is extremely ambitious, and always the same: to get at least one more person voting outside the country than there are 'official' voters inside the country. Every time we manage this, the world has changed a little bit, and it becomes harder and harder for politicians everywhere to ignore the message we're sending out: when you're elected to run your country, you become part of the team that runs the planet.
Your decisions affect all of us.