In plain English
An algorithm is a precise sequence of steps, much like a recipe, that a computer follows to turn an input into a result. In traditional software a person writes those steps by hand. In machine learning, the learning algorithm is the procedure that adjusts a model based on data, so the model effectively works out its own rules rather than having them written for it.
A worked example
A sorting algorithm takes a shuffled list of names and returns them in alphabetical order by comparing and reordering items according to fixed rules.
Common confusion
People often use algorithm and AI model interchangeably. The algorithm is the procedure; the model is the trained result that procedure produces.