BTCLovingDude,

you should really look more into how bitcoin and the blockchain works.
The "classic" blocks are within the blockchain as they adhere to the same consensus rules set forth by core.

To give you a bad analogy:

Think of clients as TVs that receive a data stream and decode it. Now if your TV can only decode material in say 720p and it receives a 4k stream it will not be able to display it.

Similarly full nodes perceive new blocks and validate them based on the rules set forth in their programming.
To complete the analogy a core node would understand and be able to decode a 720p signal regardless of whether it came from a "core" sender or a "classic" sender.
However the moment it receives a 4k signal it will not accept it and say it is invalid, only other classic nodes would consider the 4k signal valid.

In effect the network (as it is decentralized each node - or keeping with the analogy, every TV set - makes the decision for itself) would fork as a part of the clients say "this block (4k signal) is valid" while others say "this block is garbage that I don't recognize".

Here is the important part: As long as a classic node does not mine a large block (e.g. send the 4k signal) but sticks to what everyone understands (720p) it will be accepted by both types of clients.
By labelling mined blocks as "classic", miners are showing that they support these changes in the underlying consensus rules (such as bigger blocks).

The idea is to find agreement beforehand so that ideally everyone, or at least a vast majority of miners and full nodes, accept the changes by running a client that supports them.

By the way it is not 6 but > 60 blocks or else it would be 0.6%