An example:
Your instance probably doesn't know much about me because nobody there follows me. So if you want to see my actual profile and public posts, go to my instance. I suggest middle-clicking on my account name or avatar. You can then do remote interactions with me or my posts, and the UI will explain how.
Keep in mind that most days all of this works great, but a lot of servers are a bit sluggish right now due to growing as much as 10x in the last week.