If you want to let your users to enroll themselves to courses, first you have to enable Self Enrollment plugin, and second - enable Self Enrollment option on courses of your choice.
1) To enable Self Enrollment plugin:
Go to Site Administration->Plugins->Enrolments->Manage Enrol plugins and enable (open the eye) Self enrolment
If you wish that all courses added from this point forward would have Self Enrolment enabled, click Settings next to Self enrolment and mark the ckeck-box next to "Add instance to new courses".
2) To enable Self enrolment for courses added before step 1:
Open the course
On the "Course administration" expand Users and click on Enrolment methods.
Enable Self enrolment (open the eye).