An auto-edit (previously called automod(eration)) is an edit that does not go through the normal voting process, but is instead automatically approved and instantly applied. Such edits display "automatically applied" rather than the number of votes.
In general, only edits which add data to the database (e.g. adding an artist, adding track times) and edits which make minor changes to the data (e.g. changing capitalisation) are automatically applied. However, that is not always the case and determining whether or not an edit will be automatically applied is quite complex. Editors can prevent their edits from being automatically applied by ticking the "Make all edits votable" checkbox when submitting the edits.
Auto-editors are a trusted group of users who have been given "auto-editor" privileges and are able to enter a much wider variety of changes as auto-edits.
An edit which has just been submitted will normally stay open for 1 week or until it receives enough votes. An edit which is open can be voted on by other editors or cancelled by the person who submitted the edit.
This is the most common status. It means the edit was accepted and the changes were applied.
An edit which "failed vote" received more "no" votes than "yes" votes and was rejected.
No votes received
This is a historical status. It used to be used when the data quality was set to high but the edit received no votes.
Failed dependency, Failed prerequisite and Internal error
There is currently no real distinction between failed dependency and failed prerequisite, edits use them fairly interchangeably. However:
Failed dependency was originally used when the change can't be applied because the entity being edited does not exist any more, i.e. it was merged into something else, it was deleted or the original edit was cancelled.
Failed prerequisite was originally used when a change won't be applied because the data was already changed by another edit, i.e. there was already an open edit which was applied first or someone else entered an edit afterwards which was applied faster, either because it was an auto-edit or because it received more votes.
Internal error is rare but is used when an edit can't be applied for any other reason not listed above. An internal error is usually a bug which should be reported in our bug tracker.
A cancelled edit is an edit which is cancelled by the person who entered the edit.