Users could set database columns you meant to protect by adding extra fields to the data they send. This is called mass assignment: your app copies more of a user's input onto a model than you intended.
Laravel 4.1.29 fixed it by improving how column names are quoted for every database driver. See the Laravel 4.1.29 upgrade notes and the fix.
Who is affected
Apps on laravel/framework 4.0 or 4.1 before 4.1.29 with Eloquent models that protect columns with $guarded, and that pass a user-controlled array to update(), save() or similar methods.
Laravel says models that list their allowed columns with $fillable aren't affected.
What to do
Update to 4.1.29. If you can't, listing allowed columns with $fillable on your models is the setup Laravel describes as safe.
Laravel 4 stopped getting fixes long ago, so plan a move to a supported version.