What is the point of a soft fork when it's backwards compatible? I understand a soft fork occurs when changes in the Bitcoin protocol are backwards compatible, but why is that a fork? Is there really a branch or is that just a formality? Or does this give me a chance to run an older version of Bitcoin (older than the soft fork), and still be part of the system? But, again, why would I do such a thing. For example, is there any active &quot;soft&quot; branches in the network that I can transfer on? 
Thank you guys!
Seems you answer the first question yourself :-).  Yes, it's a fork as it enforces new rules. But it does allow you to run an older version of bitcoind (not recommended though, but supported) and still be part of the Bitcoin network.

is there any active &quot;soft&quot; branches in the network that I can transfer on ?

This would mean there was a network split, what a soft fork is trying to avoid.
There are still old clients running that for example do not enforce the last soft fork that occured (Segwit), but they are part of the Bitcoin network and not an alternate one because the change was backward-compatible.