An algorithm is a set of instructions, sometimes called a procedure or a function, that is used to perform a certain task. This can be a simple process, such as adding two numbers together, or a complex function, such as adding effects to an image. For example, in order to sharpen a digital photo, the algorithm would need to process each pixel in the image and determine which ones to change and how much to change them in order to make the image look sharper.
Most computer programmers spend a large percentage of their time creating algorithms. (The rest of their time is spent debugging the algorithms that don't work properly.) The goal is to create efficient algorithms that do not waste more computer resources (such as RAM and CPU time) than necessary. This can be difficult, because an algorithm that performs well on one set of data may perform poorly on other data.
As you might guess, poorly written algorithms can cause programs to run slowly and even crash. Therefore, software updates are often introduced, touting "improved stability and performance." While this sounds impressive, it also means that the algorithms in the previous versions of the software were not written as well as they could have been.