If you take the phrase “go out on a limb” literally, it would be climbing onto an unstable or fragile limb while you are climbing a tree. As an idiom, it means to state an opinion or say something that is maybe a little bit risky.

For example…

“I’m gonna go out on a limb and say it. I don’t like the Beatles!!!”

“I’m really going out on a limb here, but I’ll come to your party as long as I can finish my homework before!”