An algorithm is any well defined computational procedures that takes some value or set of values as input and produces some value or set of values as output. A mathematical functions are a kind of algorithm where it performs a procedure to come out with a value based on a problem with a defined set of input value or values.
There are also non-computational algorithms, such as directions to calling a person on the phone. The steps are sequential from picking up the phone, getting the number, dialing the number, etc. etc.
But procedures should cover all possibilities and the subsequent action it must take. Going back to the phone call example, the algorithm should include steps for situations where the phone gets a busy signal or that the phone number cannot be found.
In short, algorithms must take all situations that could arise into consideration.
Classical Computers and Quantum Computers
There are three ways to make a computer work faster. One is to make more computers (using multiple computers for one activity). Another is to make new computers faster. And the third is to make algorithms that lets computer do things faster.
Without an algorithm behind a program or application, computers won't be able to perform as it should.
