M. Mitchell (2019) calls it perhaps the most important term in computer science: a "recipe" of steps a computer can follow to solve a problem (2019, ch. 1). Logicians know its rigorous version, the notion of an effective procedure that Church and Turing formalized in 1936.
In machine learning, two algorithms coexist that are easily confused. One is the learning algorithm, written by people: the Perceptron rule, ID3 for decision trees, k-means, backpropagation with gradient descent. The other is what that algorithm produces: a model that, given an input, computes an output. The second is also a procedure, but nobody wrote it line by line. Chollet (2021) sums it up by saying that machine learning discovers the rules of a task from examples of what is expected, instead of receiving them as a program (2021, sec. 1.1.3). In Elemedex, species of the algorithm kind (Support vector machine, k-nearest neighbors…) are classical learning methods; those of the model kind are concrete products of training.
The distinction reopens a classic objection. In 1843 Ada Lovelace wrote that the Analytical Engine "has no pretensions whatever to originate anything": it can only do whatever we know how to order it to perform (Chollet, 2021, sec. 1.1.2). Turing (1950) discussed this as "Lady Lovelace's objection." A trained system does execute an algorithm someone knew how to order; but the rules it ends up applying were known to no one beforehand, and sometimes to no one afterwards (see black box). Is that enough to say it "originates" something?
It is also worth distrusting journalistic usage: a social network's "algorithm" usually designates a whole system (models, business rules, data, and engagement metrics), not a procedure.