This is the number of seconds to display the next page before logging you off of this device. (divide by 60 for minutes, 300 seconds is 5 minutes)

Setting this to, say 120, would mean that the next page will be displayed for 2 minutes before you will automatically be logged out, unless you click on a link or button on that page

You are being asked for this on every page because you indicated that you didn't want us to remember your username on this device, we take this to mean you are using a public device.