> Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity.

I.e., it's an asymptotic upper bound.

It's also interesting to compare with Ω() (Big Omega ­— asymptotic lower bound) and Θ() (Big Theta) (big-O AND big-Omega): https://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachm...

A good textbook on this subject is Introduction to Algorithms: https://www.amazon.com/dp/0262033844/ .