When you log into SharePoint using Claims Based Authentication, a cookie is written to disk to store the Claims information, which prevents you having to be authenticated each time you open a new browser or re-boot.
You can change the cookie to be session based by running this PowerShell script:
$sts = Get-SPSecurityTokenServiceConfig
$sts.UseSessionCookies = $true
You can revert back to a disk based cookie (default) by running this:
$sts.UseSessionCookies = $false