Any member or admin from an event can invite other members to an event. (Depends what is the settings of the event if member can invite then members will also be able to invite new people otherwise admin only will be able to invite new people).
Places from where member can be invited.
In these places if anyone wants to invite a existing member just start typing the name of the person inside the community field is give auto suggestions and who is inviting can select the name and click on invite. A mail as well as notification with accept decline button will be received by the invited member. By accepting only he/she can be associated with the event with a proper role mentioned.
If anyone wants to invite a new member then they have to type the full email id and confirm that. After a mail will be sent to the mail id and the new user have to signup in the system and he/she will become associated with that specific event with the mentioned role provided.