Arrays allow programmers to work with multiple similar data values efficiently. There are different types of arrays including one-dimensional, two-dimensional, and multi-dimensional arrays. One-dimensional arrays use a single index, two-dimensional arrays use two indices for rows and columns, and multi-dimensional arrays can have three or more indices. Programmers can initialize array values at declaration time or runtime, and access elements using indices. Common array operations include sorting, searching, and performing mathematical operations on arrays.