What is the laymen meaning of "sampling from a binomial distribution"? I know what is binomial distribution but I am not able to realize sampling associated with it. Further a formal statement and applications of sampling from a binomial distribution would be of great help.
Thanks.

A Binomial Distribution is that of the count of successes among a certain amount of success/failure trials;† each with an identical and independent rate of success.
So if you have a known amount of trials, $n$, all with the same probability of success, $p$, and each is independent of every other, then the count of successes is a $\mathcal {Bin}(n, p)$ random variable.
Examples:


*

*tossing the same coin a certain amount of times and counting the heads.

*rolling a certain amount of identically balanced dice and counting those showing 6

*drawing balls from an jar with replacement and shaking a certain amount of times, and counting those of a particular colour. 

*drawing cards from a standard deck with replacement and shuffling between draws a certain amount of times and counting the aces drawn.

*and so forth.


Additionally, in some cases taking a representative sample from a significantly large population and counting matches of a particular criteria may be approximated as having a binomial distribution.   Though more accurately the count will have a hypergeometric distribution.

† btw, these are called Bernoulli trials.
