Games with a purpose are games that help you learn or practice something and isn't just for pure entertainment.
An example of a game with a purpose is Typing Adventure. You have to type in the word that is given so he can get around the obstacle or go in the right direction. This game is used to help you practice your typing skills and it could be also used to teach typing. Typing Adventure appeals to mostly elementary students who are learning how to type and want to practice.
Another example is Sudoku. In this game you have to arrange the numbers 1-9 in several different boxes. Also you can't put the same numbers in the same line or same box. This makes the game difficult and teaches you how to use strategy. This game is mainly for people in high school.
An example of a game with a purpose is the Spanish word English definition. In this game you match words in different languages to their meaning in English. This helps you learn and practice Spanish and is very useful to anyone who is trying to learn another language.