Each of your "live" apps comes with a small companion program (bundled in, so there's nothing for you to do to get them) that does the tile updating every 30 minutes (plus or minus a few minutes). The updates can only use a little bit of memory and have to finish quickly (under 30 seconds), so they don't have a great impact on battery life.
You can see which apps have these "in the background" or "periodic" tasks by going in to Settings, swiping to the Applications panel, and opening the Background Tasks page. This is a list of the companion programs that we do work in the background. Note, a companion program can be active even if the app isn't pinned to the Start screen. (For example, you might want Weave to get new content regularly, but not have it pinned.) If you find an app that's annoying you, you can use this page to block the app's ability to even schedule the task to run periodically.
Two final notes that causes some confusion for some new users:
1) The main part of the app is what asks the operating system to schedule the periodic task to run. When the OS does that, the schedule is for every 30 minutes for two weeks. Usually, apps extend the schedule each time they start up. IF you have an app that works this way and you pin it so read information from its tile, but you don't ever tap the tile to go in to the app, the updating will stop within two weeks because the scheduled task will end.
2) If the periodic task is a bit buggy or slow, Windows Phone will unscheduled it -- these tasks are allowed to fail or be slow once in a while, but if they screw up two times in a row, the OS won't even try a third time. (Of course, the app itself can ask the OS to schedule the periodic task again, but that means that you have to go in to the app. Most apps don't tell you the "state" of their background task "subscription" so there's no way for you to know if the updates are running or not; Microsoft needs to do a bit of work in this area. (Mine reports "on", "off", "expired", "slow", "memory hog" or "crashed", but it's not a general-purpose app.)