The realisation of a random variable is the value that is actually observed from it, the actual observation of what happened.
In other words, the realisation of a random variable is a specific value that is returned by our random variable (a function ).
Random variables are denoted with uppercase letters (e.g. ), but their observations are denoted with lowercase letters (e.g. ).
Realisations are used when ordering random variables when we collect them as random samples.