A website I visit keeps popping up a banner at the bottom of the screen that says "Webpage wants to run Java SE runtime environment 7 update 71" from Oracle America,Inc. Then it asks to allow.
Should I allow this? Or maybe I should ask is this safe to allow?

What website is this?
Always go to the Java or Oracle website to get Java updates.
If your website is a website for a browser-based game, the game may use Java and may need the update.

I found out this is a critical security update and definitely should be downloaded. The problem is when you go to the java SE download page there are so many things there and it is not clear what download is 7u71. I will keep trying to figure out their page.

Hi Geo,
I could be wrong but another way to update your Java is to go to your Control Panel and you should see a Java Icon, double click on that and you should see an option to do an Update and that should automatically update your Java.

I am not sure about this anymore since I no longer have the Java application since the modern IE and FF browsers no longer require this, at least for all the sites I visit.

Good luck with your update problem.

@Geo It's the Runtime you want. JRE (Java Runtime Environment) under the Java SE 7u71/72 section.