Canonical Partners are proprietary software source code repositories. These are almost always free, but not Open Source.
They have been tested by Canonical, but are closed to development as they are commercial third party code.
If you check it to on, it may give you access to slightly more software than you have available. There is nothing bad about checking it and nothing really bad about not checking it.
Much of what is there is also available in a different version in the main Ubuntu repo. For example, Google Cloud and Skype are available on both, with the Canonical partners version being the closed source third party provided version.
For some, that is concerning since third party closed source code cannot be fully inspected. For this reason, default is to have it unchecked.
Why I recommend switching to “Main Server” instead of the country or regional server: I have noticed that when set to a regional server, it is not unusual for a user to experience missing packages when they try to install something. It happens often enough to be noticeable, but should not happen at all- the claim is that all servers contain the same content. The experience is something different.
In addition to this, the Main Server is the first one updated. All other servers are then updated based on a timer, which means that if you are using a server at the bottom of the list, then you may miss out on updates.
Using a local server should offer a faster download speed. But for many, it is not enough to be noticeable and given the above, preferable to use the Main Server given the risks vs speed.