Algorithms are small solutions which may be pieced together to solve large problems.
Algorithms are specific steps that perform specific tasks in a specific sequence. Algorithms are the nuts and bolts that implement the paradigms of large projects.
In war and chess, the distinction between strategy and tactics is crucial to performance in either. Strategy is the art of large scale planning, tactics are the small scale actions that implement large plans.
In computer programming, paradigms such as procedural programming and object oriented programming compete as strategies to planning large, extensive solutions to large, challenging problems. Yet those large solutions must be implemented with specific, precise chunks of code that make the large solutions possible. These larger paradigms and strategies require smaller, specific bundles of instructions that may be somehow linked together to make the large strategies work.
In computer programming, modularization is the art of breaking large problems into smaller problems through incremental segmentation of those larger problems. By solving the smaller problems, and then arranging and linking those smaller solutions into larger solutions, large problems get solved.
In practice, an algorithm of a computer program is a chunk of code that solves a problem that can be solved at one sitting. It may take five minutes or five hours but not five days to solve. In practice, the problem is small enough that it can be solved by one person in one waking session.
Algorithms may be simple and straight forward, or they may also be brilliant and elegant and convoluted in design. Algrorithms are the glue of problem solving.