Windows 10, and in particular also Windows 10 Mobile, allows you to have all your devices synchronized: therefore, for example, if you add some preferences in the browser on one device, you will find also on the browser of every other device you own (you registered your Windows account while configuring them) when you logon with your Microsoft account, … and the same for every other setting you may have set.

However there are situations where this automatic synchronization, that is configured by default, is not very nice.
For example you may want to have on one PC your Microsoft account user with the O.S. in English, while on your tablet you want it in your native language (e.g. Italian) … and this because, may be, you use your main PC for programming while your tablet for hobby and you want Cortana to work properly (see Problems running Cortana on your Windows 10 PC?).
Or may be you give your wife/son/daughter your “old” Lumia, because you bought the newest model 😉 … and you don’t want to configure it again from start…  and/or possibly you may want to use it occasionally for your purposed. To change device owner, at least actually, you have to reset completely the device and start from zero:  it is true that, if your wife/son/daughter had already a Windows Phone/Windows device, recovering a backup saved on cloud makes the new setup easier … but it may take some times especially if you had installed many apps and configured several email accounts, APNs and so on!!

So it is clear that in some cases you may want to stop some kind of automatic synchronizations …
In the first example I did, related to PC/tablet, it is sufficient to set to OFF the synchronization of the language in Settings -> Account, as I explained in this post, otherwise every time you change the language of the O.S. on one device, it will be changed also on the other one (at next restart … so it could be hard, at the beginning, to understand what it is happening!). May be you could want to disable some other kind of synchronization there listed:

Settings ->Synch your settings

For the second example, related to smartphones, you have to do the following:

1. Disable the notifications for all the email accounts that are not related to the user that usually is using that device (e.g. your wife/son/daughter): on the contrary also those notifications will be listed in the notification center … and this is boring! Obviously you could also delete that accounts, but may be it can be useful to leave them configured, just in case you have to use them in special situations (e.g. your phone stop working because it falls down or drains off!).
2. Disable the synchronization of SMS messages among devices (Settings -> System -> Messages), otherwise all the SMS, both the sent and received one by all  devices each one with a different phone number, will be listed in the Messages [IT: Conversazioni] page.
   

   SMS for my wife and for me are received on both devices owned by me (also the sent one even it is not shown in this screenshot)

   So you must to set to OFF the following “Synchronize messages among devices” [IT: “Sincronizza i messaggi tra i dispositivi“] option:

   

   Settings -> System -> Messages

3. May be you could also want to disable in the device owned by you but not usually used by you, the option Settings -> Account -> Sync your settings, as shown in the following:

Settings -> Account -> Sync your settings