Suppose you have 10 teams, and each of them has their own slideshow. You are running a competition between your teams, and you would like to create a notification that triggers whenever someone makes a sale. You could simply create one single notification, and add all slideshows to it, but then all of them would receive notifications about all your teams. What you want instead is for each slideshow to receive only the notifications relevant to it's team. You could achieve that by creating 10 notifications, each with one team in it, but that's a lot of work.
This is where home slideshows come in. When editing a team, you can select some home slideshows, which will allow you to create one single generic notification that will only show up on the team's home slideshow that triggered the notification.
Notifications for registrations:
When a registration triggers the notification, that registration's team will be used to find the home slideshows. If the registration does not have a team, all of the registration's member's teams will be used.
Notifications for formulas:
When a formula triggers the notification, all of the teams set on the trigger will receive the notification.