It’s simply, really – an algorithm is a set of instructions with which to solve problems. We tend to think of algorithms in terms of artificial intelligence, but we humans actually use algorithms to solve everyday problems, for example, to count how many people there are in a room. 

A search algorithm, then, is an algorithm which searches and sorts data, finding items with specific characteristics in a collection of items (a database). Search engines use (mathematical) search algorithms to find the information you're looking for when you type in a search query

Need a simpler explanation? Watch David J. Malan’s ‘What’s an Algorithm’ Cartoon: