The purpose of lessons learned is to bring together any insights gained during a project that can be usefully applied on future projects.
Lessons learned are one of the most powerful and cost-effective project management tools available today. If you consider that many projects make the same mistakes time and again, you soon realise that lightning does strike twice, often more frequently.
It's said there are no new project management sins, just old ones repeated. It's also said that we don't learn the lessons from past projects, and this must be true, otherwise why would we keep making the same old mistakes.