Which of the following describes a binary tree?

A binary tree is specifically defined as a data structure in which each node can have at most two children, commonly referred to as the left child and the right child. This unique characteristic allows for efficient organization and traversal of data. In many applications, binary trees are used to implement binary search trees and heaps, which facilitate quick data retrieval and sorting.

The other descriptions do not accurately represent a binary tree. For instance, a linear structure that only holds integers does not align with the hierarchical nature of trees, as trees are not linear and can store various data types. A collection of unordered elements describes a data structure like a set or list, which does not impose a tree structure. Lastly, direct indexing refers to data structures such as arrays, where elements can be accessed via an index, unlike the navigation through nodes in a binary tree.