Attachments are prim objects that are worn by an avatar. Common uses for attachments include hair, shoes, tails, capes, weapons and wings. Avatars that don't look human are almost always made using attachments.
Here's the official help page on attachments.
When worn, they are automatically phantom and not physical. Unless you script, all that means is that big hair won't prevent you from walking thru a doorway.
To wear an object, right-click on the object, pick "Wear" or "Add", and watch it appear on your avatar. You can do this from your inventory or on a rezzed object.
To take one off, pick Detach. You can do this by clicking on the attachment and right-clicking and choosing "Detach", or by clicking on the object from your inventory and choosing "Detach"
If an object hasn't had a attachment point set, it defaults to appearing on the avatar's right hand. It used to default to their skull; this is where those "newbie with a box on their heads" jokes come from.
If you don't want it on your right hand, you can choose another attachment point. You can't pick another attachment point for an object you are currently wearing, so if you're wearing it, take it off first. Right-click on the object, then pick "Attach to" and choose a point from the list. This also sets the object's attachment point, so next time you wear it the attachment will appear there.
Rez a pose stand. When your avatar uses one, it holds them almost motionless so you can make fine adjustments to your attachments. They're scripted objects, so they might not work if you're in a no-scripts area.
Open your edit tool and click on a worn attachment. Notice that there's several kinds of grid references in the drop down. I usually use "Attachment Point" when adjusting the position of an attachment. This sets all your edit arrows and hence your changes to be relative to the attachment point.