When you receive a request that needs to be responded to an additional box will appear on the right hand side of the Dashboard screen with the name of the request.
A 'Requests' dropdown link will also appear in your top bar and a red notification will inform you of the amount of requests you have to respond to. Click on this to respond. Requests include invitations to groups or events, as well as announcements of tasks. Your request alert will stay until it is dealt with.
Notifications sit on the toolbar next to requests. Notifications differ from requests in that they are alerts to tell you when content that you're following is updated. You'll also receive notifications for direct @messages within comments.