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I'd prefer as little formal definition as possible and simple mathematics.

Big -O notation is an Asymptotic Notation for the worst case or ceiling of growth for a given function. It provides us with an asymptotic upper bound for the growth rate of the runtime of an algorithm.

for example

Worst-case time complexity of linear search is O(n).

for example

Worst-case time complexity of linear search is O(n).

Big-O notation basically is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. It is an Asymptotic Notation for the worst case, which is also the ceiling of growth for a given function. It provides us with what is called an asymptotic upper bound for the growth rate of runtime of an algorithm or program.

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