It means you're supporting an idea or action alone, without others backing you up. He was out on a limb, insisting the project would work despite the team's doubts.
Pro Tip 2/3
Exposed Position
You are in a vulnerable situation where you might be criticized or fail. By predicting an unlikely outcome, she was really out on a limb.
Pro Tip 3/3
Figurative Sense
This idiom does not refer to a physical position but to a metaphorical stance. He's out on a limb with that controversial opinion.