When you log into a Google site like GMail, Google also logs you into all your various accounts Google accounts - such as YouTube. In order to be logged into a site, Google sets a cookie in your browser.
This is fine for most of their properties which are on the
docs.google.com, etc). However a website can only set and read a cookie for it's own domain -
google.com can't set a cookie for
youtube.com. To get around this, as part of the login process Google will redirect you through
accounts.youtube.com to log you into YouTube - and typically your country specific domain if you are outside the US (e.g. I get logged into
google.com.au as well).
The full login process is described in this SO answer, it dates from 2009 but most of it should still hold true.