From what I understand:

Pros of hosting your own instance:

• control over your data (privacy)
• performance (your instance is probably less busy/faster than lemmy.world, because it has to handle less people, so things load faster)
• it cool

Cons of hosting your own instance):

• maintenance
• federation cost increases for the network (i.e. All instances that host communities you are subscribed to (i.e. Lemmy.world), now need to send (federation) updates to your new instance). Note that as more people start using your instance, it is better for the network.
• you have to have a server running somewhere, which costs money’s.
• you need a max 20 character domain name.