Yes, it's not something made for User Experience (on contrary) but to improve security.
Imagine this situation.
You're accessing one secure site, home page is not secure (it uses HTTP protocol) to greatly reduce server CPU usage (because homepage is requested very often by random users and search engines or because it contains non-critical material). You enter your credentials and you login then you're redirected to a HTTPS encrypted connection and now you're sure no one will be able to read or alter your data packets.
However if your network is unsecure someone may sniff data you send. This is not a problem with HTTPS because it's encrypted but - do you remember? - you logged in using HTTP and you've redirected to HTTPS after that. If attacker sniffed your credentials (in plain text) then he can effectively act as a man in the middle. HTTPS connection is secure after it has been initiated, not before.
In this very specific case certificates for homepage and login page are issued to different companies (and I'd guess the one for homepage is a generic certificate issued to hosting service provider).
OK but why new window? Can't we just reuse existing window/tab and start a new HTTPS session? AFAIK for three reasons:
1) To prevent possible attacks. This topic is out of my knowledge then please refer to Triple Handshakes and Cookie Cutters: Breaking and Fixing Authentication over TLS.
2) To make clear to user that a new secure connection is started. It's maybe the only UX point.
3) To be sure (or greatly reduces chances that) browser bugs and plug-ins loaded by previous pages aren't still loaded in same session/process. Especially if you don't force your users to use latest full-patched browser version then this is main reason to still open a new page nowadays.
EDIT: if we ask ourselves "is this still required nowadays?" then answer is probably "no, maybe it's not" but banks (and company which offers financial services) tends to be little bit conservative about security especially if they don't limit their users to use latest full-patched browser (when they even still have in use Windows XP computer with Internet Explorer 7)...