An algorithm in computer science is a set method for solving certain types of problems. Take the sort for example. There is the Bubble Sort, Heap Sort, Selection Sort, etc. Some faster than others.
A data structure is a manner in which data is organized on a machine. This usually refers to linked lists, binary trees, arrays, stacks, queues, etc. In a linked list for example, one data items points to the next data item and so on.