If you're trusting, you tend to believe what people tell you. A trusting friend will tell you her deepest secrets and trust that you'll keep them to yourself.
Use the adjective trusting to describe people who always see the best in others. A trusting child believes everything you tell him and follows where you lead. A trusting dog will follow your commands and stick by your side. The verb trust means "to believe or have faith," and both words come from the Old Norse traust, "help or confidence," and are closely related to the Old English treowe, "have faith or confidence."