A non-linear data structure is a type of data structure where data elements are not arranged sequentially or linearly, unlike linear data structures. In non-linear data structures, elements are stored in a hierarchical or network-based structure that does not follow a sequential order. Non-linear data structures are used to solve complex problems where data cannot be arranged in a linear manner. Examples of non-linear data structures include trees and graphs. Non-linear data structures allow efficient searching, insertion, and deletion of elements from the structure. Non-linear data structures are not easy to implement as compared to linear data structures, but they make better use of system memory. Linear data structures are simple to execute because of their linear organization. Examples of linear data structures include arrays, linked lists, queues, and stacks. Linear data structures are useful for simple data storage and manipulation, while non-linear data structures are useful for representing complex relationships and data hierarchies.