If you load your 2014 project in in 2016, the whole project will be converted to 2016.
This normally goes Ok (no bad experiences myself).
When saving that converted file it will be permanently converted into 2016 and can not be opened with Revit 2014 (or 2015) anymore.
In the forums you read that, in some rare intances, the conversion gives problems or that some objects does not work well anymore in the newer revit version or that project unworkable..
So it always good practice to keep a copy of the 2014 version save so that you can go back if needed.
Linked Revit files will not be automatically converted and have to be loaded/converted separately.
It is not absolutely necessary to convert linked files. However every time the linked file gets loaded it will be temporarily converted. Depending on the sizes and the amount of links this can take a long time.
If you are working with other parties you have to make sure that they are also working with Revit 2016 otherwise they will not be able to load/link the project in their projects anymore.
If working with workshared files and the implications you can have look over HERE. As this is a bit more lengthy
Louis

Please mention Revit version, especially when uploading Revit files.