"Invitations" are cards (or, more recently, e-mails) that you send to people. An invitation announces an event like a wedding or a party, and lets you know that you're welcome to come to it.
The word "invitation" can also mean asking someone to come to an event. When you use "invitation" in this way, it often comes in these phrases:
- To "extend an invitation to" someone means to invite them.
- To "accept an invitation" means to say "yes".
- To "have an open invitation" means that you are invited to go somewhere any time you want to.
Written "invitations" can be plural, but a spoken "invitation" usually isn't.