The Source tab is part of the FishEye Plugin and is used for integration with SVN. The Commits tab is part of the Jira DVCS Connector Plugin and is used for integration with gits (Git, Mercurial, BitBucket etc.).
Atlassian enables these tabs by default.
If either FishEye or Jira DVCS Connector plugin is not installed, the Source or Commits tab will not be visible on the Issues page.
To hide the Source tab from the Issues page, disable the FishEye Plugin:
To hide the Commits tab from the Issues page, disable the Jira DVCS Connector Plugin: