There are 5 basic phases .. the ones you have listed, plus controlling.
Initiation - This is typically a very short phase where senior management decides to move forward with the project. The project sponsor writes the project charter describing the high level goals and names the project manager.
Planning - The project manager assembles the project team and they respond to the project charter with a detailed plan including scope (what will actually be done), time, cost, resources, and risk plan. A good plan addresses all 9 PMBOK Guide knowledge areas.
Execution - Once the project sponsor and/or senior management approve the plan, the actual work begins.
Controlling - Often a certain amount of controlling is done in parallel with execution. This is where the work is supervised (project manager monitors progress according to plan and takes corrective action as necessary) or quality assurance is conducted. Controlling phase also manages the risks.
Closing - Delivery of the final project is confirmed. All financial information is reconciled and historical information about the project is archived for future use.
There is obviously a lot more to each phase and each phase contains many processes, however I believe the above to be a good summary. Let me know if you have any further questions.