Trustworthy describes something you can believe in — it's completely reliable. Your favorite newspaper can be trustworthy — they always print the truth — and people can be trustworthy too. You only tell your secrets to a trustworthy friend.
Breaking apart the word trustworthy gives you a clue to its meaning. It combines the common word trust, which describes something you can rely on, and the word worthy, which describes something that deserves respect. So something — or someone — that's trustworthy deserves your trust. In an election, you'll likely vote for the most trustworthy candidate because you believe she'll keep her promises. If you're trustworthy, that means you're reliable: you do what you say you're going to do.