And in plain english 
The standard recovery on the S4 is very limited (clearing the cache and restoring a stock ROM is about all it allows), PhilzTouch recovery offers a lot more options including installing system files (an area the end user cannot normally access) and building an "image" of the system "as is" so the phone can be restored the way I want it in a couple of minutes.
Phoenix ROM itself has a number of tweaks and quite a few of the S5 features ported over (eg, keyboard, launcher, Flash player support, etc.
In short, it's what the phone should have been to start with.
How are you liking the Note 4? I was seriously considering it before getting the S5
Haven't got it yet.
My brother came over today and has a Note 3 running Aryamod v1.5 (custom version of Lollipop), now I've seen that I'm out tomorrow to get a Note 4 (that's all they have in stock now) so I can do the same.
It's a bit bigger physically than the S4/S5, but size isn't really an issue for me now I'm not in my normal working environment.
Everything I tried works quite well, and it's a darn site quicker than when it was on the standard ROM as well as the battery lasting much longer between charges.