When you're talking about the real world, "project an image" means to shine light onto a surface to show a picture, like a slide show or a movie in a movie theater.
When you're talking about a person's actions and personality, to "project an image of ___" means to show other people a certain quality or personality trait. This phrase is only used for positive qualities, though. That's because "projecting an image" is something that a person does on purpose. Some qualities that people often project include:
project an image of confidence
project an image of authority (this person seems to be powerful and in-control)
project an image of wealth (this person seems to be rich)
project an image of approachability (you feel like you can talk to this person easily)
For negative qualities, instead of saying that a person "projects an image of ___", you can say that they "come off as ___":
He comes off as rude and hard to work with.