Data Structures define the schematic arrangement or organization of data. Many a times the performance of an algorithm heavily depends on the kind of data structure used to solve the problem at hand.
An important and initial step in problem solving is to decide how to represent data in memory and on file.
An algorithm always works on a defined data structure. In fact the running time of algorithms must be specified in reference to a data structure. Few of the graph algorithms like Shortest Path etc can demonstrate a lot of difference in their running type based on the underlying data structures.
Data Structures are the building blocks to a good application design. It is an intensive and complicated task to get the data structure right. One good example is the origin of interval trees.