With setter initialization you construct an empty object and then use setter methods to setup various properties as you go. (An alterative to ConstructorInitialization.)
So create a person with firstname, lastname, and a collection of favorite bars we might see something like
#ruby mf = Person.new mf.firstname = 'Martin' mf.lastname = 'Fowler' mf.add_bar "Turner's Oyster Bar" mf.add_bar "Square and Compass"
This approach gives you the maximum flexibility in wiring up objects, allowing you to provide just the collaborators you need for a specific usage.
It frees you from having to set all the values at once - which is handy if some objects are only available at later times.
Each method call is compact, which avoids the problem of long parameter lists to constructors and an array of different constructors to choose from.
Marko Schulz reminded me that setter methods have names that explain their use for the new object - this is a noticeable advantage over ConstructorInitialization in most languages these days which only have positional parameters. Constructor parameters with very general types (strings etc) can easily get very cryptic.