An invitation is a request, a solicitation, or an attempt to get another person to join you at a specific event. You need an invitation to go to the Academy Awards, even if you're George Clooney.
When you ask people to attend a party, visit your beach house, or witness your marriage, you invite them — using the verb — and you've given them an invitation. An invitation can be delivered as a verbal request, a beautifully engraved card, or even puffs of smoke behind an airplane. If you give invitations to two hundred of your closest friends to attend your Mardi Gras party, you’d better make a lot of jambalaya.