When iOS 5 was released, Newsstand came with it as a central location for all of your newspapers and magazines on your iPhone and iPad. One of the big features of Newsstand is the ability to have your subscriptions update automatically when a new issue is available. For example, The Daily updates every day while my subscription to The Economist updates every week.
To make sure that your subscriptions are updating automatically, you need to make sure you have the feature enabled. By default this should be enabled when you install a newspaper or magazine app that uses Newsstand but I have found cases where updates to the app disable it for some reason. Also, if you have had situations where a magazine or newspaper is not updating regularly, you can turn off the auto update then turn it back on and it seems to cure the issue.
The automatic updating is found in Settings under the Store section. At the top is the Automatic Downloads section for Music, Apps and Books (this assures that if you buy a new app on your iPhone that it is automatically downloaded to your iPad for example). Below that will be your subscriptions from Newsstand. Make sure that each one that you want to automatically download up-to-date content is turned on.
Keep in mind that content is downloaded only when WiFi is available. If your iPad is a 3G/4G version or if you are using your iPhone, new magazine and newspaper content will not be downloaded using the data network of your carrier.
Also remember that most subscriptions for Newsstand apps also take advantage of Notification Center to let you know of breaking news or updates or if a new edition of that subscription is available. In some cases this is a little redundant but for some apps, like The Daily, it can be quite handy. As always, you can adjusted and/or disable the Notification Center settings for each of your Newsstand apps in the Notification Center section of Settings.