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Big O notation is a mathematical representation that describes the upper limit of an algorithm's time complexity or space complexity in relation to the size of the input data. It essentially provides a high-level understanding of how the performance of an algorithm scales as the size of input increases, thus focusing on the efficiency and resource usage of an algorithm rather than specific implementation details.

When discussing the complexity of algorithms, Big O notation helps categorize them based on their growth rates, such as constant time, logarithmic time, linear time, quadratic time, and others. This information is crucial for developers to predict how algorithms will perform under various conditions and to make informed decisions about which algorithm to use for specific tasks.

Although Big O can be related to execution time and memory usage, it does not directly measure those aspects; rather, it measures how they change with input size. The number of inputs doesn't capture the essence of what Big O notation conveys, as it does not specify a precise number of inputs but rather the relationship between input size and algorithmic efficiency. Therefore, the focus of Big O notation is best encapsulated by the complexity of algorithms.