This all depends upon your settings. If you have your settings to "PRIVATE" and people have to specifically request to follow you, then only those on that person's follow list will see the messages [tweets]
One reason "Why I Think Twitter Is Special"
When you sign up, you have the option of keeping your account public (the default account setting) or Protecting your account. Public accounts have profile pages that are visible to everyone, while Protected accounts manually approve those who views its Tweets.
It's up to you. Your followers read your updates, and anyone else who comes across them in a search. Your Twitter profile is public by default; if you're hesitant to have strangers read your updates, protect your profile to approve followers and keep your updates out of search.