Data Structures are ways to collect and store data. And why do we do this? Because we want to manipulate/understand that data in an efficient and effective manner. Stacks, queues, linked lists, heaps, beaps, treaps, trees, etc. are all examples of data structures.
An algorithm is a procedure that aims to solve a particular problem/task. Think of it as a recipe. You lay out ingredients for a dish and the dish is only complete and tasty when the ingredients are added at a certain time and in a certain ORDER. Same goes for an algorithm.