Well, when someone says he has sent you invitation to Google Plus, it means they added you to any of their circles in Google+.
Now if you go to http://Google.com/+ or http://plus.google.com/ and login with your gmail id (which was invited) Google will let you in (provided that Google+ is not over capacity! bad luck sometimes! you know!) and you can enjoy using Google plus and inviting your friends on google plus.
Please note: Once someone says they invited you and you didn’t receive any notification email ask them to share something to your circle on google plus, this will send notification email to you. (and don’t forget to do this practice when you invite someone)
If you are having error on google plus login screen saying:
Already invited? We’ve temporarily exceeded our capacity. Please try again soon.
Don’t panic and keep trying again and again until it gets you in.