Algorithms are small problems to solve with code, sometimes requiring cleverness, often requiring loops, and even more often requiring different kinds of data structures to solve, such as arrays and hashes to name a few. They are very commonly used as interview questions.
Remember that algorithms go hand in hand with data structures.
Chek out Algosaur, a graphic guide to algorithms!
Take these free Coursera courses: Algorithms I and II.
- Introduction to Algorithms, by Thomas H. Cormen
- Algorithms, by Robert Sedgewick
- The Art of Computer Programming, Vol. 1: Fundamental Algorithms, by Donald E. Knuth
- Grokking Algorithms, a great book in Python on algorithms.