What is Google+1
The Google+1 button is your public recommendation of a website or webpage. It's essentially the Facebook Like button but for your Google account.
Here is Google's explanation:
"The +1 button is shorthand for 'this is pretty cool' or 'you should check this out.'
Click +1 to publicly give something your stamp of approval. Your +1's can help friends, contacts, and others on the web find the best stuff when they search."
Who sees my Google+1 rating?
Anybody that Google sees you connected with (through Gmail, Google Plus, etc) will see that you +1'd a website when searching in Google. If you have a Google Plus account, it also shows everything you have +1'd in your profile.
Can I see who +1'd my website?
Unfortunately, no you can't see who +1'd your website.
For more information on Google +1, you can check out this site: http://www.google.com/+1/button/