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An array in C++ is a data structure that allows you to store multiple elements of the same type in a contiguous memory layout. The array elements are accessed using an index, with the first index usually being zero. This data structure is especially useful when you need to organize data that is related, such as values from a series of measurements or a list of objects.

For instance, when you declare double a[3], you're creating an array named 'a' that can hold three elements of type 'double'. To manipulate and access the elements of the array, you will primarily use the indexing operation, which involves placing the index of the desired element inside square brackets next to the array name, such as a[0] or a[2]. Arrays are incredibly efficient for sequential data processing and are a fundamental aspect of C++ programming.

Initializing an array means setting it up with values before you start using it in your program. In C++, array initialization can be done in multiple ways, such as listing all elements inside curly braces at the time of declaration.

For example, in the code double a[3] = {1.1, 2.2, 3.3};, the array 'a' is immediately initialized with the specific double values in the given order. Remember, if you don't initialize an array explicitly, its values will be indeterminate (or zero-initialized for static and global arrays). Proper initialization ensures that you avoid unexpected results due to garbage values.

Output streams in C++ are used for producing output and sending it to various destinations like the console, a file, or a string buffer. The most used output stream is cout, which typically sends data to the standard output, generally the screen.

In conjunction with the insertion operator (<<), cout can be used to print text, numbers, or the content of variables. When you use cout<<a[0]<<' '<<a[1]<<' '<<a[2], you are streaming the contents of the array 'a' to the console with spaces in between, providing a human-readable format. The stream also permits control over formatting output, making it flexible and robust for various output needs.

Element assignment in an array means assigning a new value to a specific position within the array. This action alters the state of the array moving forward in the execution of the program.

In the given example, a[1] = a[2]; demonstrates this concept: the element at index 1 (originally 2.2) is being reassigned the value of the element at index 2 (which is 3.3). Post this assignment, the element at index 1 will now hold the value 3.3, effectively duplicating the value that was at index 2. Understanding element assignment is crucial for manipulating arrays, enabling sorting, updating, and handling data dynamically during program execution.