Can anyone explain this to me? Does this mean a remote computer is accessing my computer.
1 Answer
No, this does not mean that a remote is accessing your computer.
As it says in the screen shot "Ensures the identity of a remote computer". This means that with the issued certificate you can be confident that your computer is contacting its intended target, in your example this would be a server owned and authorized by facebook.com.
There is plenty of information out there on how SSL/TLS works. You should start here in order to better understand what is going on and appeal to your curiosity.
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