Can I get a notification on my iPhone when I receive a certain email? I need to be able to reply to just 1 email that I irregularly receive within seconds of it arriving.  I want my iPhone to start vibrating etc. when it arrives.

Email is from info@meetup.com (the meetup website).  Problem is I only want to be notified when 1 of about 100 emails/month arrive.

That target email can only be identified based on a text string in its body content together with its email subject line. It's not (not able to be) coming from a special email address nor is it able to be set to go to a unique address for myself.  (They use 1 email they send from and I am limited to 1 email address to use to receive all 100 emails.)

I use gmail and Apple Mail on the Mac and have an iPhone.  But my Mac is not on all the time.

How do I get my iPhone to vibrate at me when this email arrives?
It is not possible on your iPhone. I searched for a bit if there was a third party email application which had this feature.

If I where you I would look into IFTTT (If This Then That). I'm on my phone now so could not try if you could read body text from emails. But there is a trigger->action: Get a notification when you get a new email with a specific label.

I'm not a Gmail user, but I guess you can make rules. 


Make a rule that looks for incoming mail and scan for the subject or text in body and apply that label to that new email message. 
Make a trigger->action in IFTTT. Let IFTTT watch your Gmail for any new messages with that specific label. IFTTT wil send you a push notification.