The default option is "public" - anyone can see your tweets. You can protect your tweets, but that means you also have to authorise every single person who wants to view them, and they can't re-tweet your tweets.

There's also a search function. For example, I'm not on Twitter, but I was able, with a two-word query, find out what was happening when the park opposite us sprouted two police helicopters with searchlights. And again when local roads were closed by a big factory fire, I was able to follow people's tweets and see which roads were jammed with displaced traffic.