A profile contains a set of configuration data.
When the M1KE boots up, it loads the information from one of the profiles into memory and uses that to configure itself. When you change profiles, it reboots and loads the newly selected profile into memory instead. It also "remembers" which profile you last selected, and if you power the M1KE off entirely, when you turn it back on, it will boot into whatever profile you had last selected. (There is an "advanced mode" setting called "Always use profile #1 on power on", which is normally off. If you turn this setting on, then like it says it will always start with profile #1 when booting up from a full power-off.)
Each profile contains things like which "connector" (i.e. "REF/XRF" for D-STAR, "Homebrew/MMDVM" for DMR, etc.) to use and what destination to send messages to (i.e. reflector/repeater for D-STAR, talkgroup for DMR, etc.).
Profiles also contain wi-fi networks and passwords. There's an "advanced mode" setting called "Save settings below to all configuration profiles" which is normally turned on. When this is on, then like it says it will store the wi-fi network names and passwords into ALL profiles when you click "Save". This makes it act like there's only one list of wi-fi networks, but if you turn this setting off you can have different wi-fi networks stored in each profile. This can be useful if you want to use different profiles based on your location - maybe one at home, one when you're tethered to your phone, one when you're visiting family, and so forth.
I think the only truly "global" information, stored in the M1KE but not in a profile, is the "owner information" - your call sign, DMR ID, NXDN ID, and the "I have an amateur radio license" flag.
@HA2NON please correct me if I'm wrong about any of this ... and also consider adding this information to a "welcome to M1KE" section in the documentation. It took me a bit of trial and error to get my head wrapped around how profiles worked, and I design and write software (and documentation) for a living.
FWIW on my M1KE I have a profile for D-STAR and a profile for Brandmeister. The "Save wifi settings to all profiles" setting is turned on (so all profiles have the same wifi information), and the wifi networks are ordered as:
1: my phone
2: my phone
3: another hotspot device I sometimes use
4: my home wifi
The first network is there twice because when you enter a wifi network by hand (using the M1KE's on-screen keyboard), that overwrites network #1, and I didn't want to have to re-enter my phone's network information again.
While I'm using the D-STAR profile, I can change which reflector (or repeater) I'm connected to, using the "Quick setup" function, and the M1KE "remembers" which reflector/repeater I'm connected to when I reboot the unit. For example, if I was using profile 1 and connected to REF037C when I shut the M1KE down, the next time I turn it on, it will boot into profile 1 and connect to REF037C again automatically. The same seems to be true for the Brandmeister profile - if I was subscribed to 3100 when I shut down, it subscribes to 3100 again automatically when it boots back up.
As for "Favourites" ... for D-STAR I use them to hold the reflectors and repeaters I normally use (i.e. REF037C, REF030C, etc.) and for DMR I'm using them for hold the talkgroup numbers I normally use, so I don't have to remember a bunch of number codes (3100, 93, 98, 3112, 310997, etc.) The menu settings involved in connecting to different reflectors or talkgroups, have options to use these "Favourites" instead of having to select or enter them by hand.
Hopefully some of this will be helpful.