Here's a breakdown of the meaning:
* "Limb" refers to a branch of a tree.
* "Going out on a limb" implies venturing away from the safety and security of the trunk of the tree, where you are less likely to fall.
Examples:
* "I'm going out on a limb here, but I think this project is going to be a huge success."
* "She went out on a limb by criticizing the boss in front of everyone."
* "The company went out on a limb by investing in a new technology that wasn't proven."
The idiom can be used in a variety of contexts to describe someone who is taking a chance, expressing an unpopular opinion, or making a bold prediction.