Short answers, pulled from the story.
Positive feedback occurs when the outcome of a process reinforces the inciting process to build momentum. It causes the magnitude of a perturbation to increase over time through exponential growth or chaotic behavior.
Regenerative circuits were invented and patented in 1914 for amplifying weak radio signals. These circuits can multiply gain by 1,000 or more but often become unstable and start to oscillate at very high gains.
During childbirth, oxytocin causes uterine contractions that stimulate the hypothalamus to produce more oxytocin until the baby is born. In blood clotting, injured tissue releases chemicals that activate platelets which release more chemicals to form a rapid cascade.
Markets with social influence demonstrate that popular products tend to become even more popular through this mechanism. George Soros advanced the theory of reflexivity where price changes are driven by a positive feedback process involving investor expectations reinforcing movement.
The main positive feedback in global warming is the tendency of warming to increase water vapour in the atmosphere leading to further warming. Other examples include melting ice changing albedo surface reflectivity and releasing methane from hydrates or peat bogs.