Array
Elementary
An array is an arrangement of objects in rows and columns.
High school
An array is a set of items arranged in rows and columns (or in a list, or in a block with more directions).
Undergraduate (programming)
An array is a collection of elements indexed by tuples of integers $(i_1, \dots, i_k)$ in a rectangular index range. The number $k$ of indices is the number of axes (or dimensions) of the array.
Notes
An array is a data structure. Its entries can be any type, and no arithmetic is implied.