In a binomial experiment to say that each trial is independent of the other trials means that the outcome of one trial does not affect the other trial.
An experiment with a set number of independent trials and just two results is referred to as a binomial experiment.
To say that in a binomial experiment, each trial is independent of the other trials means that the outcome of one trial does not affect the other trials.
This means that whatever we get in the first trial, does not affect the outcome of the second or any other trial.
For example, in the tossing of a coin 10 times, the outcome of the first trial doesn't affect any of the other nine trials.
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