Friend, 
What happens when you boost something?:
It will help the content move up the page to increase visibility.
It will add the content to your boost list, which can be found in your profile.
Warning, your boost list is public to anyone who visits your profile.It will add +1 to the user's reputation.
Your followers on federated microblogs (e.g. Mastadon) will see the boosted content in their Home feed beneath a banner telling them you boosted it.