Each method in the Office.js APIs is marked with an API set designation, which you can see when using them.
These API sets match the Office versions that the add-in will support. http://dev.office.com/reference/add-ins/office-add-in-requirement-sets contains a list of requirement sets and the platforms on which they are supported.
Excel 2016+ (and its Office Online and Mac/iOS equivalents) are the only platforms that support any of the new Office 2016 host-specific API sets (ExcelApi, WordApi, etc.). The API version number (1.1, 1.2, and 1.3) refers to API improvements that were made after Office 2016's RTM build (which shipped with 1.1 out-of-the-box). Customers that subscribe to Office 365 have access to those updates (home or business). Customers who purchased Office 2016 as a disk/MSI product will only have the original 1.1 APIs.
The requirement sets can be put to two different uses. You should identify any API sets that your add-in 100% depends on in your manifest file. That way, the add-in won't even be proffered on the "Insert/Manage Add-ins" dialog for Office versions that don't support that particular API set. On the other hand, if you're only using a few APIs in the set, and could do without (even if it's a bit of a degraded experience), you can do the "light-up scenario". That is, you will list the lowest possible version that you do need, and then use a runtime check to detect whether a particular API set is available.
if (Office.context.requirements.isSetSupported("ExcelApi", 1.2 )
range.format.columnWidth = 25;
For a related answer, see Neat ways to get environment (i.e. Office version)