Notation that tells how fast an algorithm is.
When you need to choose an algorithm, there are always trade-offs. E.g. you need a search algorithm that is both fast and correct (on its' implementation). “simple search” (going through all elements from an array) is simple to implement and hard to have bugs - but it takes too much time to run the bigger the array. Although “binary search” is a little harder to implement and may have bugs on the implementation, it takes much less time to run if the array is bigger.
Run times for binary search and simple search don’t grow at the same rate. With more items to search into, binary search will only take a little more time to run. Otherwise, simple search will take a lot more. As the list of numbers gets bigger, binary search becomes A LOT faster than simple search.
Too choose wisely between algorithms, you have to know 2 things:
Big-O notation doesn’t tell you the speed in seconds, but in the number of operations - in the worst case scenario - the maximum number of operations to find an element.
Big-O notation examples:
“Traveling salesperson” is a problem where you have a salesperson that needs to go e.g. to 5 cities, traveling the minimum distance. That is an algorithm that takes O₍n!₎ time - the slowest possible. It is one of the unresolved problems in computer science.