You can have your app look for new asset bundles from a server and download them if necessary using the WWW class.

From the iphone docs:

var download : WWW;

    var url = "http://somehost/somepath/someassetbundle.assetbundle";

    download = new WWW (url);

    yield download;

    assetBundle = download.assetBundle;

    if (assetBundle != null)
    {
        // Alternatively you can also load an asset by name (assetBundle.Load("my asset name"))
        var go : Object = assetBundle.mainAsset;

        if (go != null)
            instanced = Instantiate(go);
        else
            Debug.Log("Couldnt load resource"); 
    }
    else
    {
        Debug.Log("Couldnt load resource"); 
    }

You can then save the data to a documents folder on the device

Again from the docs:

public static string GetiPhoneDocumentsPath () 
        { 
                // Your game has read+write access to /var/mobile/Applications/XXXXXXXX-XXXX-XXXX-XXXX-XXXXXXXXXXXX/Documents 
                // Application.dataPath returns              
                // /var/mobile/Applications/XXXXXXXX-XXXX-XXXX-XXXX-XXXXXXXXXXXX/myappname.app/Data 
                // Strip "/Data" from path 
                string path = Application.dataPath.Substring (0, Application.dataPath.Length - 5); 
                // Strip application name 
                path = path.Substring(0, path.LastIndexOf('/'));  
                return path + "/Documents"; 
        }

You can also simply download a texture or some text from a website and use them directly in your game without using asset bundles if you prefer. You do this by setting up a new WWW and storing the returned text as a string with www.data