Whatever you think you think gamification is or what it is for, if you have used it it is usually for one reason – to increase engagement with something. You may not have defined engagement as such, you may have spoken about active participation, or learning transfer, or productivity increase. However, they all point in one direction – to encourage people to do more of something or to do it better.
Some of the projects you have done or seen may have been long term focused, looking to increase intrinsic motivation of participants, others may have just been short term campaigns using simple mechanics to reward activity.