When you log in, the system wants to know if it's a valid account or whether it should kick you back to the login screen.
According to Mike Sego, a former Gmail engineer, "shva" is an acronym for "should have valid authentication". Apparently, the parameter is only included after a successful authentication.
1 is the default value applied to the parameter check. It's also a shorthand way for programmers to say
true, like when you have successfully logged in.
The other part,
#inbox, tells Gmail to load up your inbox as the first screen. You can change that to one of the other folders (or even labels you've created) to load them up.
https://mail.google.com/mail/?shva=1#sent will show your Sent folder items.
https://mail.google.com/mail/?shva=1#label/narwhals will load up your "narwhals" label.
Gmail, like many web services, serves a standard interface that will change to show only your information and data when you've logged in.
The particulars are referenced on their end through the use of an ID from the cookies or sessions generated after the login screen.