Chernoff bounds and Monte Carlo algorithms

Question

One of Wikipedia examples of use of Chernoff bounds is the one where an algorithm $A$ computes the correct value of function $f$ with probability $p > 1/2$. Basically, Chernoff bounds are used to bound the error probability of $A$ using repeated calls to $A$ and majority agreement.

I don't understand how, to be frank. It would be nice if somebody could break it down piece by piece. Moreover, does it matter whether $A$ is a decision algorithm or can return more values? How are Chernoff bounds in general used for Monte Carlo algorithms?