The Church-Turing Thesis (a meta-mathematical statement) asserts that any "reasonable" method of computation is equivalent to any other, i.e., any algorithm that can be implemented in one computational device can be implemented in any other.
As a consequence, the notion of algorithm is independent of the choice of implementation.
In cooking, some recipes are more difficult to do than others, because they take more time to finish or have more things to keep track of.
It is the same for algorithms, and algorithms are better when they are easier for the computer to do.
When we look at algorithms as a way of solving problems, often we want to know how long it would take a computer to solve the problem using a particular algorithm.
When we write algorithms, we like our algorithm to take the least amount of time so that we can solve our problem as quickly as possible.
In computing, an algorithm is a precise list of operations that could be done by a Turing machine.
For the purpose of computing, algorithms are written in pseudocode, flow charts, or programming languages. There is usually more than one way to solve a problem.
Given a fixed method of implementing algorithms (for example, the Turing machine, or a fixed programming language) we may ask how much computational resources an algorithm consumes.
In particular, it is often of practical importance to know how much time and how much memory a given algorithm consumes.