I'm our new Senior Warden
My rector asked me to be his Senior Warden. I was pretty intimidated because this is the first time I've even been on a vestry.
The previous Senior Warden tells me Fr. Wilson makes it really easy, and so far he has. I'm hoping for a smooth two years.
Here's my church, btw. The parish is 145 years old, and the building we're in is 105 years old. It used to be THE Episcopal church in the East Bay, with Kaisers populating the pews. Currently we're a very diverse congregation, including LGBT families.
http://www.stpaulsoakland.org
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I'm pretty much supposed to support the rector and, by extension, his family. That could include telling him something he doesn't want to hear, but I doubt that'll come up with my rector.
During times between rectors (Lord, please don't let that happen), the Senior Warden is the chief executive. I understand that under very extreme conditions, the SW can administer the eucharist. That won't happen with a bishop right across the bay.
Various rectors have asked the SW to do certain things, but my rector doesn't seem to have extra jobs for me. Thank heaven, because I'm already full up with jobs around the church. 
I love my rector and my church. I pretty much say yes to everything they ask unless I know I'm unqualified.