The Promote action allows you to cross promote another campaign and award actions for completing it.
Examples:
You're running a multi-day competition and you want to award extra entries to users who had entered the previous day
You have 2 other campaigns running and you want to make users aware of them, and award extra entries for entering them
You've partnered with 5 other brands and you want to cross promote each others campaigns (and only award entries when they enter each)
You're running a campaign with other Bloggers, instead of having all the actions in 1 campaign each Blogger might create their own and then chain them together with Promote actions