When you work together on shared goal, you collaborate. If you don't just split a project up evenly but work together on creating solutions, you collaborate.
Inside the word you see co-labor, or "working together." Cooperation is simply splitting up the work and getting it done. Collaboration is when you brainstorm, create, and share possible solutions. During World War II, however, Nazi collaborators were sharing ideas with the wrong side. In today's pop music scene, collaboration means featuring a guest star on a record, and it's often a surefire way to boost sales.