I have a project ABCD with a start is 04/15/2016 and the project's end date is 04/30/2016.

But I can make the activity has a start date and an end date of 25/05/2016 and 05/30/2016.

These dates are validated or planned dates?

Yes, projects have validated. But I do not know how to planned, because it is not for the manually enter

Validated dates are the commitments you wish to respect.
Validate dates on project put no constraints on activities.
It works the other way roud : it is activities that will determine start and end dates of project.

As Ad said, the day of activity used to determine the start and end of the project.On my project, I set the start date and end date is 04/01/2016 04/20/2016. So my activities can make out the end of the project, ie I can create activities with a start and end date is 05/05/2016 05/20/2016. Meanwhile, my project end date will depend on the closing date of the last activity? Is it right?
There's something I do not understand much. 🙁
I think the day of the activities will be in the start date and end date of the project rather.
Thanks for the help 🙁

my project end date will depend on the closing date of the last activity? Is it right?

Yes

I think the day of the activities will be in the start date and end date of the project rather.

No, valiaded start-end dates are just what you expect (or wish, or committed to). IT is the activities, with work, constraints, that will determine dates for project.