Quality profile of sonar is a set of check rules, like the rulesets of Checkstyle. You can create/modify/backup/rename/delete a profile at [Settings -> Quality Profiles] as Administrator. Creating a profile means importing check rules from a xml file. On the contrary, "backup" a existing profile means save it(as a xml file) to disk. You can edit the profile under the "Coding rules" tab, and link it to a specific project under the "Projects" tab.
Once defined some profiles, you can use it in a sonar runner by specify it in sonar-project.properties file:
sonar.profile=profile_name
You also can specify a profile to a project at "Configuration"(at the upper-right corner of the dashboard of the project). See Analysis Parameters for all 4 ways to specify profile for a project, and a full list of parameters you can specify in sonar-project.properties.