What is the documents directory (NSDocumentDirectory)?

Swift 3 and 4 as global var:

var documentsDirectory: URL {
    return FileManager.default.urls(for: .documentDirectory, in: .userDomainMask).last!
}

As FileManager extension:

extension FileManager {
    static var documentsDirectory: URL {
        return `default`.urls(for: .documentDirectory, in: .userDomainMask).last!
    }

    var documentsDirectory: URL {
        return urls(for: .documentDirectory, in: .userDomainMask).last!
    }
}

I couldn't find the code in the doc suggested by the accepted answer but I found the updated equivalent here:

File System Programming Guide :: Accessing Files and Directories »

- (NSURL*)applicationDataDirectory {
    NSFileManager* sharedFM = [NSFileManager defaultManager];
    NSArray* possibleURLs = [sharedFM URLsForDirectory:NSApplicationSupportDirectory
                                 inDomains:NSUserDomainMask];
    NSURL* appSupportDir = nil;
    NSURL* appDirectory = nil;

    if ([possibleURLs count] >= 1) {
        // Use the first directory (if multiple are returned)
        appSupportDir = [possibleURLs objectAtIndex:0];
    }

    // If a valid app support directory exists, add the
    // app's bundle ID to it to specify the final directory.
    if (appSupportDir) {
        NSString* appBundleID = [[NSBundle mainBundle] bundleIdentifier];
        appDirectory = [appSupportDir URLByAppendingPathComponent:appBundleID];
    }

    return appDirectory;
}

It discourages use of NSSearchPathForDirectoriesInDomain:

The NSSearchPathForDirectoriesInDomains function behaves like the URLsForDirectory:inDomains: method but returns the directory’s location as a string-based path. You should use the URLsForDirectory:inDomains: method instead.

Here are some other useful directory constants to play with. No doubt not all of these are supported in iOS. Also you can use the NSHomeDirectory() function which:

In iOS, the home directory is the application’s sandbox directory. In OS X, it is the application’s sandbox directory or the current user’s home directory (if the application is not in a sandbox)

From NSPathUtilities.h

NSApplicationDirectory = 1,             // supported applications (Applications)
    NSDemoApplicationDirectory,             // unsupported applications, demonstration versions (Demos)
    NSDeveloperApplicationDirectory,        // developer applications (Developer/Applications). DEPRECATED - there is no one single Developer directory.
    NSAdminApplicationDirectory,            // system and network administration applications (Administration)
    NSLibraryDirectory,                     // various documentation, support, and configuration files, resources (Library)
    NSDeveloperDirectory,                   // developer resources (Developer) DEPRECATED - there is no one single Developer directory.
    NSUserDirectory,                        // user home directories (Users)
    NSDocumentationDirectory,               // documentation (Documentation)
    NSDocumentDirectory,                    // documents (Documents)
    NSCoreServiceDirectory,                 // location of CoreServices directory (System/Library/CoreServices)
    NSAutosavedInformationDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 11,   // location of autosaved documents (Documents/Autosaved)
    NSDesktopDirectory = 12,                // location of user's desktop
    NSCachesDirectory = 13,                 // location of discardable cache files (Library/Caches)
    NSApplicationSupportDirectory = 14,     // location of application support files (plug-ins, etc) (Library/Application Support)
    NSDownloadsDirectory NS_ENUM_AVAILABLE(10_5, 2_0) = 15,              // location of the user's "Downloads" directory
    NSInputMethodsDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 16,           // input methods (Library/Input Methods)
    NSMoviesDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 17,                 // location of user's Movies directory (~/Movies)
    NSMusicDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 18,                  // location of user's Music directory (~/Music)
    NSPicturesDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 19,               // location of user's Pictures directory (~/Pictures)
    NSPrinterDescriptionDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 20,     // location of system's PPDs directory (Library/Printers/PPDs)
    NSSharedPublicDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 21,           // location of user's Public sharing directory (~/Public)
    NSPreferencePanesDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 22,        // location of the PreferencePanes directory for use with System Preferences (Library/PreferencePanes)
    NSApplicationScriptsDirectory NS_ENUM_AVAILABLE(10_8, NA) = 23,      // location of the user scripts folder for the calling application (~/Library/Application Scripts/code-signing-id)
    NSItemReplacementDirectory NS_ENUM_AVAILABLE(10_6, 4_0) = 99,       // For use with NSFileManager's URLForDirectory:inDomain:appropriateForURL:create:error:
    NSAllApplicationsDirectory = 100,       // all directories where applications can occur
    NSAllLibrariesDirectory = 101,          // all directories where resources can occur
    NSTrashDirectory NS_ENUM_AVAILABLE(10_8, NA) = 102                   // location of Trash directory

And finally, some convenience methods in an NSURL category http://club15cc.com/code/ios/easy-ios-file-directory-paths-with-this-handy-nsurl-category

This has changed in iOS 8. See the following tech note: https://developer.apple.com/library/ios/technotes/tn2406/_index.html

The Apple sanctioned way (from the link above) is as follows:

// Returns the URL to the application's Documents directory.
- (NSURL *)applicationDocumentsDirectory
{
    return [[[NSFileManager defaultManager] URLsForDirectory:NSDocumentDirectory inDomains:NSUserDomainMask] lastObject];
}

Your app only (on a non-jailbroken device) runs in a "sandboxed" environment. This means that it can only access files and directories within its own contents. For example Documents and Library.

See the iOS Application Programming Guide.

To access the Documents directory of your applications sandbox, you can use the following:

iOS 8 and newer, this is the recommended method

+ (NSURL *)applicationDocumentsDirectory
{
     return [[[NSFileManager defaultManager] URLsForDirectory:NSDocumentDirectory inDomains:NSUserDomainMask] lastObject];
}

if you need to support iOS 7 or earlier

+ (NSString *) applicationDocumentsDirectory 
{    
    NSArray *paths = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES);
    NSString *basePath = paths.firstObject;
    return basePath;
}

This Documents directory allows you to store files and subdirectories your app creates or may need.

To access files in the Library directory of your apps sandbox use (in place of paths above):

[NSSearchPathForDirectoriesInDomains(NSLibraryDirectory, NSUserDomainMask, YES) objectAtIndex:0]