I am concerned that the public consciousness is growing ever more aware of algorithms, without any real understanding of what algorithms actually are.

There is a distinction between a computer program and an algorithm.

The public experiences buggy software implementations, with the result that the press reports on the disturbing influences over our lives. There is no discussion of provable correctness, resource consumption, the halting problem and so on.

I've been at a loss for years as to how to adequately explain algorithms to people who don't know anything about computers. Commonly I saw that "an algorithm is a general method of accomplishing a specific task on a computer. An algorithm for changing a flat tire would work on any kind of car." yet that fails to satisfy.