A computer algorithm is a step by step procedure/instruction that enables a computer to execute specific tasks, or solve a problem. such problems might be logical and mathematical in nature. An algorithm is geared at solving a specific task, they are finite in nature, every algorithm must terminate or end.
An example is the quick sort algorithm, know as a divide and conquer type of algorithm, it divides a list into two by selecting a pivot, after which the sub list are then sorted recursively.