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An array size declarator is a part of the syntax used when declaring an array in a programming language. It specifies the size (number of elements) that an array will store. The size is typically provided as an integer value.

The primary purpose of the array size declarator is to allocate the appropriate amount of memory needed to store all the elements of that array in a program's memory. By specifying the size, the programming language's compiler or interpreter can reserve the memory needed to hold the array's elements.

The usage of an array size declarator depends on the programming language syntax. Here are a few examples: 1. **C/C++**: In these languages, the array size declarator is included within square brackets, like so: ``` int myArray[5]; ``` The above code defines an integer array named 'myArray' with a size of 5 elements. 2. **Python**: Although Python uses lists instead of fixed-size arrays, one can create a list with a pre-defined size using the following code: ```python my_list = [None] * 5 ``` This creates a list called 'my_list' with 5 elements, initialized with 'None' values. 3. **Java**: In Java, arrays are objects created using the 'new' keyword. An example array declaration: ```java int[] myArray = new int[5]; ``` The above code declares an array of integers called 'myArray' with a size of 5 elements.