1. To put in a specified position or arrangement; place: set a book on a table; set the photo next to the flowers. 2. a. To put into a specified state: set the prisoner at liberty; set the house ablaze; set the machine in motion. b. To cause to begin an action: The noise set the dog to barking.
When mathematicians talk about a set, they sometimes want to know how big a set is (or what is the cardinality of the set). They do this by counting how many elements are in the set (how many items are in the bag).
I have a set of porcelain figurines depicting characters from Shakespeare's plays. A set is a group of things, where every single one of them has a certain purpose.