What does it mean to be signed in to the devices below? So I am signed in with my company's Apple ID and I noticed I am signed in to several devices according to Apple website. What exactly does that mean in terms of capabilities and features?
It just helps you monitor things. You’d want to know if someone had your password and signed in. You also can run into device count limits for playing purchased music, so you need somewhere to see those counts as well. 

There’s not much to do other than know it signed in and clear items when you think they are retired or erased or donated/sold.