Which terminates on the other side where everything is plaintext again. https is a transport level protocol, so it protects you from people (trivially) snooping on your data in transit but anybody at google with enough clearance has access to that data.
I'm not worried, it's just that the gggp of this comment mentioned that search history is protected by a password and so it 'should be safe from prying eyes.'
All I did was point out that that data is stored on a server somewhere else and that there are lots of eyes that could be prying there.
I'm sure that there are plenty of people that are concerned about their internet use being monitored, for instance, dissidents and other people that have legitimate reasons to be afraid of having their search history lifted in the future.
Interesting reading on the subject of subpoenas of search records:
Any website that you use could store all kinds of data about you without even telling you. Not to mention your ISP, who knows everything! At least Google is making it clear via Google History that they do have the means to do it.
Assuming no MITM attack, yes. Of course they can still see what hosts you're connecting to for your HTTPS sessions, just not the content going back and forth.